AlgebraicLoopGroupHoop Package ALGHCA.

Algebraic Loops, Groups, Hoops, Cliffords. R. H. Beresford.

Exit

Off[General::"spell",General::"spell1",Part::"partd",
Syntax::"com",Less::"nord"]
(*That allows similar names and nulls to be used*)

NotebookFileName[](*Based on 5/3/11 15.47 version sent to MathSource. db96
Sent to EP 15.40 23/4/12*)

1. Introduction.

This package develops Algebraic Loops, Groups (associative loops), symmetry-conserving generalised-sign vector-division (hoop) algebras & Clifford (anti-commutative hoop) algebras. The data is validated and the procedures are demonstrated in ALGHCAtest.nb, which also provides an outline of hoop algebra.. A glossary is provided in ALGHCAGloss.nb.
I apologise for the 1970’s style programming and many clumsy structures. This package is intended as an archive of the development of Hoop algebras, and the emphasis is on accuracy rather than elegance. My intention is to carve it into a number of re-written packages when the package is stable.

2. Version, Copyright notice.

Version="ALGHCA 3rd April 2012 ";

© Copyright 2003-2012 Roger Herbert Beresford, 15, Brook Lane, Nanpantan, Loughborough, Leics, LE11 3RA, England. 
Considerable effort has gone into checking this work, but some errors probably persist. No responsibility will be accepted for any problems arising from its use. Permission is granted to distribute this file for any purpose except for inclusion in commercial software or program collections. This copyright notice must remain intact.

3. Revisions.

Developed from MathSource 31st. Dec. 2010 version. 
28/2/11 New section 9.6 added, giving access to db96 (or db36 in development version), with IrreducibleAffordingMatrixRepresentations (irreps) and justification via Representation Theory.
14/8/11 Some minor corrections included.
3/9/11 Group names changed to GAP standard, with disambiguation.
12/9/11 NonPC cycle formulations added as 10th. loop entries.
18/9/11 loop and gap inversions coordinated, reo & gapPerm added.
17/1/12 xC reverted to C. toVector removed
24-27/2/12 minor corrections, isoCay, dic, loop[[24]].
10/3/12 restored C5 shape as a comment.
14/3/12 irrep replaces smat. D3 and x corrections to loop. fold, addSigns added.
18/3/12 𝕒𝕒 replaced by 𝕒2 etc. A few slow or faulty id’s removed. 840 correct, 63 not unique.
22/3/12 revised fold, sml and smReal converted to irrepl. 16/4 asa & alph.

4. Keywords.

Algebras, additive elimination, anti-commutative algebras, blades, bivectors, Cayley-Dickson, Cayley-tables, Clifford, Clifford-like, conservative algebras, continuous orbits, disparate vectors, determinants, directors, dot product, Frobenius-conservation, GAP, generalized signs, generators, groups, hoops, hoop shapes, hoop sizes, index-tables, irreducible representations, irreps, isomers, isomorphs, isotopes, Jordan product, Lie product, loops, monovectors, multivectors, Moufang Loops, non-associative algebras, octonions, primal numbers, partial-fraction division, partial-fraction-division-by-zero, pseudo-scalar, quasigroups, representation theory, renormalization, remainders, roots of unity, rotors, shapes, sizes, signed-tables, trivectors, uncertainty, vecs, wedge products, zero-vectors.

5. Warnings.

Many new concepts transcend and revise those current mathematical beliefs that are solely based on real and complex numbers (which are specialisations of the more general Hoop & Clifford concepts).
Global effects - Cl,el2,el3,el,gel,genel,gLoop,gName,Jo,Li,matel,mm,nn,gi,gp,R1,Rr,sg,sh,
smax,strep are names that are altered by various routines.

6. Limitations.

Only a random selection of loops with over 73 elements are included in the loop database; they will not be uniquely identified, or given the correct gnnmm, by id. All 267 64-element groups are present, but some lack unique identification and generation. (More large groups are accessed via the db96 database). Associativity is (deliberately) not tested by id, so non-associative tables may be wrongly identified as groups (idc tests for conservation, but not associativity, before attempting an identification). Clifford hoops and named signed-tables may be isotopes. (Isomorphs correspond to renaming elements; isotopes involve changing some element signs so that the structure, but not the details, of the shape is conserved). Geometric Algebra is rudimentary. Geometric Analysis is not yet implemented.

7. Nomenclature, 2-letter abbreviations.

Group names are those used by GAP, with “x” eliminated,  “:”  and “.”converted i or j to disambiguate all names. (About half of the original GAP names are ambiguous.) Evaluating from left to right makes “(“ &  “)” redundant. The Mathematica group naming conventions are ignored.

TWO LETTER ABBREVIATIONS.
ca=Create Cayley Table from formula,
cd=Create Cayley Table by doubling,
Cl is an anti-commutatve Clifford algebra, Cl=Jo+Li,
cLoop=Create Clifford Table,
co=Compose Cayley Tables,
ds=Formalae in Dozalcons,
el2,el3,e33,el element names as double-struck symbols,
fa=Find el2 determinant,
fp=Find 2^n determinant,
gd=Loop data, active loop.
ge=make loop from 𝕒 etc,
gi=group inverse data,
gp=loop multiplicity data,
id=Table identitification,	
Jo is a Jordan (dot) product that is not conservative	
Li is a Lie (wedge) product that is not conservative,
ma=make loop from matrices,
md=Moufang Doubling,
mg=make loop from matrix list,
mp=Make Protoloop,
ms=make signed table from u2 etc,
mm=No. of elements in target loop,
nn=index of target loop in loop[[mm]],
pe=make Cayley Table from permutations,
Rl,Rr=Left and right remainders that conserve sizes,
rU=conversion root of Unity rules for sh,dS etc.,
s3,s4,s5=permutations defining groups S3 to S5,
sd=size data, containing el,rofu,gi,gp,sh,
sg=subgroup indices,
sh=shape of active loop,
tf=TraditionalForm,
ts=toSignedLoop,
u2,u3,u4=unitary monomial matrices used by ma, mg, ms.

8. Set up the ALGHCA package, usage.

8.1 Begin, ALGHCA Usage.

BeginPackage["ALGHCA`"];

ALGHCA::usage="ALGHCA`(previously GroupLoopHoop.m etc) is a package that creates two databases:-
 (1) loop contains over 900 algebraic loops, including all groups (associative loops) with up to 73 elements
 (2) db96 contains almost all groups with up to 96 elements.
It generalizes signs & creates & manipulates Groups & 'Moufang Loops' (ordered division quasigroups) as index-tables (Cayley tables with indices as elements) and signed tables (e.g. the complex & Quaternion multiplication tables). It also sets up symmetry-conserving partial-fraction-division algebras (Hoops) based on loops, and provides procedures & tests for division, powers, roots, polar-dual formulations & many loop properties.
Special (but incomplete) treatment is provided for Clifford (Geometric) Algebras (the anti-commutative sub-set of hoops). Most physically significant algebras (including ℝ, ℂ, hyperbolic, Pauli or Minkowski, quaternion, octonion, & Clifford algebras) are Hoops; many other algebras (Jordan, Lie, Wedge etc) are subsets of hoop algebras. Routines to access and use them (as hoops) are provided.
Fundamental concepts:-
Algebraic loops (which include groups and hoops as subsets) deal with unsigned coefficients. Generalized signs (powers of r'th roots of unity) arise from 'folding' or 'collapsing' loops that have Cr (the r'th cyclic group) as a central subgroup. {+,-} and {+,I,-,-I} correspond to r=2 and r=4. Negation (unary -A) should not be conflated with subtraction (binary B-A), which is the r=2 case of additive elimination. (A-B) is often found where the general meaning is the symmetric difference |A-B|; I is often found where the general meaning is the (often anti-commutative) pseudo-scalar 𝕀.
Hoops conserve 'sizes' (conjugate factors of the generalised determinant of their Cayley table; the irreducible matrix representation of a group is called irrep and provides sizes).
Vectors may have sizes that are zero. On multiplying/dividing vectors with disparate zeroes, sizes that are missing from the result are 'ejected' as remainders that maintain conservation. The result has been 'projected' onto a lower-symmetry sub-algebra. 
Noether's theorem suggests that algebras that do not conserve symmetries are unlikely to be relevant to physics.";

8.2 Alphabetic list of Usage for symbols, functions and procedures.

I have failed to find an alternative to the following tedious usage for double-struck element names.

ø::usage="Scalar or null element";𝕒::usage="Symbol in sh etc.";𝕒2::usage="";𝕒2::usage="";𝕒3::usage="";𝕒4::usage="";𝕓::usage="";𝕓2::usage="";𝕔::usage="";𝕔2::usage="";𝕕::usage="";𝕖::usage="";𝕗::usage="";𝕘::usage="";𝕒𝕓::usage="";𝕓𝕒::usage="";𝕒𝕓2::usage="";𝕒𝕓2::usage="";𝕒2𝕓::usage="";𝕒2𝕓::usage="";𝕒3𝕓::usage="";𝕒4𝕓::usage="";𝕒5𝕓::usage="";𝕒6𝕓::usage="";𝕒7𝕓::usage="";𝕒8𝕓::usage="";𝕒9𝕓::usage="";𝕒10𝕓::usage="";𝕒11𝕓::usage="";𝕒12𝕓::usage="";𝕒13𝕓::usage="";𝕒14𝕓::usage="";𝕒15𝕓::usage="";𝕒16𝕓::usage="";𝕒17𝕓::usage="";𝕒18𝕓::usage="";𝕒19𝕓::usage="";𝕒20𝕓::usage="";𝕒21𝕓::usage="";𝕒22𝕓::usage="";𝕒23𝕓::usage="";𝕒24𝕓::usage="";𝕒25𝕓::usage="";𝕒26𝕓::usage="";𝕒27𝕓::usage="";𝕒28𝕓::usage="";𝕒29𝕓::usage="";𝕒30𝕓::usage="";𝕒31𝕓::usage="";𝕒32𝕓::usage="";𝕒33𝕓::usage="";𝕒34𝕓::usage="";𝕒35𝕓::usage="";𝕒36𝕓::usage="";𝕒37𝕓::usage="";𝕒38𝕓::usage="";𝕒39𝕓::usage="";𝕒40𝕓::usage="";𝕒2𝕓2::usage="";𝕓𝕔::usage="";𝕒𝕓2𝕔::usage="";𝕓2𝕔::usage="";𝕔3::usage="";𝕓2𝕔::usage="";𝕓𝕔2::usage="";𝕓2𝕔2::usage="";𝕒𝕔::usage="";𝕒𝕔2::usage="";𝕒4𝕔::usage="";𝕒7𝕔::usage="";𝕒11𝕔::usage="";𝕒2𝕔::usage="";𝕒𝕓𝕔::usage="";𝕒𝕓𝕔2::usage="";𝕒𝕓𝕔3::usage="";𝕒5𝕓𝕔::usage="";𝕒2𝕓𝕔::usage="";𝕒𝕓2𝕔::usage="";𝕒2𝕓𝕔::usage="";𝕒2𝕓2𝕔::usage="";𝕒𝕓2𝕔2::usage="";𝕒2𝕓2𝕔2::usage="";𝕕2::usage="";𝕒𝕕::usage="";𝕒2𝕕::usage="";𝕓𝕕::usage="";𝕒𝕓𝕕::usage="";𝕒2𝕓𝕕::usage="";𝕒𝕓2𝕕::usage="";𝕒2𝕓2𝕕::usage="";𝕒𝕕2::usage="";𝕔𝕕::usage="";𝕒𝕔𝕕::usage="";𝕒2𝕔𝕕::usage="";𝕒𝕔2𝕕::usage"";𝕓𝕔𝕕::usage="";𝕒𝕓𝕔𝕕::usage="";𝕒2𝕓𝕔𝕕::usage="";𝕒2𝕓2𝕔𝕕::usage="";𝕒𝕖::usage="";𝕒2𝕖::usage="";𝕒𝕖2::usage"";𝕓𝕖::usage="";𝕒𝕓𝕖::usage="";𝕒2𝕓𝕖::usage="";𝕒2𝕓2𝕖::usage="";𝕔𝕖::usage="";𝕒𝕔𝕖::usage="";𝕒2𝕔𝕖::usage="";𝕓𝕔𝕖::usage="";𝕓2𝕕::usage="";𝕓2𝕖::usage="";𝕓𝕖4::usage->"";𝕒𝕓𝕔𝕖::usage="";𝕒2𝕓𝕔𝕖::usage="";𝕒𝕓2𝕕::usage="";𝕒𝕓2𝕔𝕖::usage="";𝕒𝕓2𝕖::usage="";𝕓2𝕔𝕕::usage="";𝕒2𝕓2𝕔𝕖::usage="";𝕕𝕖::usage="";𝕒𝕕𝕖::usage="";𝕒2𝕕𝕖::usage="";𝕓𝕕𝕖::usage="";𝕓2𝕕𝕖::usage="";𝕓𝕕2𝕖2::usage="";𝕒𝕓𝕕𝕖::usage="";𝕒2𝕓𝕕𝕖::usage="";𝕒𝕓2𝕕𝕖::usage="";𝕒2𝕓2𝕕𝕖::usage="";𝕔𝕕𝕖::usage="";𝕒𝕔𝕕𝕖::usage="";𝕒2𝕔𝕕𝕖::usage="";𝕓𝕔𝕕𝕖::usage="";𝕒𝕓𝕔𝕕𝕖::usage="";𝕒2𝕓𝕔𝕕𝕖::usage="";𝕒2𝕓2𝕔𝕕𝕖::usage="";𝕒𝕗::usage="";𝕒2𝕗::usage="";𝕓𝕗::usage="";𝕒𝕓𝕗::usage="";𝕒2𝕓𝕗::usage="";𝕒2𝕓2𝕗::usage="";𝕔𝕗::usage="";𝕒𝕔𝕗::usage="";𝕒2𝕔𝕗::usage="";𝕓𝕔𝕗::usage="";𝕒𝕓𝕔𝕗::usage="";𝕒2𝕓𝕔𝕗::usage="";𝕒2𝕓2𝕔𝕗::usage="";𝕕𝕒::usage="";𝕕𝕓::usage="";𝕕𝕔::usage="";𝕕2::usage="";𝕕𝕖::usage="";𝕕𝕗::usage="";𝕒𝕕𝕗::usage="";𝕒2𝕕𝕗::usage="";𝕓𝕕𝕗::usage="";𝕒𝕓𝕕𝕗::usage="";𝕒2𝕓𝕕𝕗::usage="";𝕒2𝕓2𝕕𝕗::usage="";𝕔𝕕𝕗::usage="";𝕒𝕔𝕕𝕗::usage="";𝕒2𝕔𝕕𝕗::usage="";𝕒𝕔𝕕𝕗::usage="";𝕓𝕔𝕕𝕗::usage="";𝕒𝕓𝕔𝕕𝕗::usage="";𝕒𝕓2𝕔𝕕𝕖::usage="";𝕓2𝕔𝕕𝕖::usage="";𝕓2𝕔𝕖::usage="";𝕒2𝕓𝕔𝕕𝕗::usage="";𝕒2𝕓2𝕔𝕕𝕗::usage="";𝕒𝕔𝕕𝕗::usage="";𝕒2𝕔𝕕𝕗::usage="";𝕒𝕖4::usage="";𝕖𝕗::usage="";𝕒𝕖𝕗::usage="";𝕒2𝕖𝕗::usage="";𝕓𝕖𝕗::usage="";𝕒𝕓𝕖𝕗::usage="";𝕒2𝕓𝕖𝕗::usage="";𝕒2𝕓2𝕖𝕗::usage="";𝕔𝕖𝕗::usage="";𝕒𝕔𝕖𝕗::usage="";𝕒2𝕔𝕖𝕗::usage="";𝕓𝕔𝕖𝕗::usage="";𝕒𝕓𝕔𝕖𝕗::usage="";𝕒2𝕓𝕔𝕖𝕗::usage="";𝕒2𝕓2𝕔𝕖𝕗::usage="";𝕕𝕖𝕗::usage="";𝕒𝕕𝕖𝕗::usage="";𝕒2𝕒𝕕𝕖𝕗::usage="";𝕓𝕕𝕖𝕗::usage="";𝕒𝕓𝕕𝕖𝕗::usage="";𝕒2𝕓𝕕𝕖𝕗::usage="";𝕒2𝕓2𝕕𝕖𝕗::usage="";𝕔𝕕𝕖𝕗::usage="";𝕒𝕔𝕕𝕖𝕗::usage="";𝕒2𝕔𝕕𝕖𝕗::usage="";𝕓𝕔𝕕𝕖𝕗::usage="";𝕒𝕓𝕔𝕕𝕖𝕗::usage="";𝕒2𝕓𝕔𝕕𝕖𝕗::usage="";𝕒2𝕓2𝕔𝕕𝕖𝕗::usage=""
𝕒𝕘::usage="";𝕓𝕘::usage="";𝕒𝕓𝕘::usage="";𝕔𝕘::usage="";𝕒𝕔𝕘::usage="";𝕓𝕔𝕘::usage="";𝕒𝕓𝕔𝕘::usage="";𝕕𝕘::usage="";𝕒𝕕𝕘::usage="";𝕓𝕕𝕘::usage="";𝕒𝕓𝕕𝕘::usage="";𝕔𝕕𝕘::usage="";𝕒𝕔𝕕𝕘::usage="";𝕓𝕔𝕕𝕘::usage="";𝕒𝕓𝕔𝕕𝕘::usage="";𝕖𝕘::usage="";𝕒𝕖𝕘::usage="";𝕓𝕖𝕘::usage="";𝕒𝕓𝕖𝕘::usage="";𝕔𝕖𝕘::usage="";𝕒𝕔𝕖𝕘::usage="";𝕓𝕔𝕖𝕘::usage="";𝕒𝕓𝕔𝕖𝕘::usage="";𝕕𝕖𝕘::usage="";𝕒𝕕𝕖𝕘::usage="";𝕓𝕕𝕖𝕘::usage="";𝕒𝕓𝕕𝕖𝕘::usage="";𝕔𝕕𝕖𝕘::usage="";𝕒𝕔𝕕𝕖𝕘::usage="";𝕓𝕔𝕕𝕖𝕘::usage="";𝕒𝕓𝕔𝕕𝕖𝕘::usage="";𝕗𝕘::usage="";𝕒𝕗𝕘::usage="";𝕓𝕗𝕘::usage="";𝕒𝕓𝕗𝕘::usage="";𝕔𝕗𝕘::usage="";𝕒𝕔𝕗𝕘::usage="";𝕓𝕔𝕗𝕘::usage="";𝕒𝕓𝕔𝕗𝕘::usage="";𝕕𝕗𝕘::usage="";𝕒𝕕𝕗𝕘::usage="";𝕓𝕕𝕗𝕘::usage="";𝕒𝕓𝕕𝕗𝕘::usage="";𝕔𝕕𝕗𝕘::usage="";𝕒𝕔𝕕𝕗𝕘::usage="";𝕓𝕔𝕕𝕗𝕘::usage="";𝕒𝕓𝕔𝕕𝕗𝕘::usage="";𝕖𝕗𝕘::usage="";𝕒𝕖𝕗𝕘::usage="";𝕓𝕖𝕗𝕘::usage="";𝕒𝕓𝕖𝕗𝕘::usage="";𝕔𝕖𝕗𝕘::usage="";𝕒𝕔𝕖𝕗𝕘::usage="";𝕓𝕔𝕖𝕗𝕘::usage="";𝕒𝕓𝕔𝕖𝕗𝕘::usage="";𝕕𝕖𝕗𝕘::usage="";𝕒𝕕𝕖𝕗𝕘::usage="";𝕓𝕕𝕖𝕗𝕘::usage="";𝕒𝕓𝕕𝕖𝕗𝕘::usage="";𝕔𝕕𝕖𝕗𝕘::usage="";𝕒𝕔𝕕𝕖𝕗𝕘::usage="";𝕓𝕔𝕕𝕖𝕗𝕘::usage="";𝕒𝕓𝕔𝕕𝕖𝕗𝕘::usage="";𝕔𝕒::usage="";𝕔𝕓::usage="";𝕒𝕔2::usage="";𝕖𝕒::usage="";𝕒5𝕓𝕔::usage="";𝕒2𝕕::usage="";𝕒𝕕3::usage="";𝕒𝕓𝕒𝕓::usage="";𝕒3𝕓𝕔::usage="";𝕒𝕔3::usage="";𝕓3𝕔::usage="";𝕒5𝕔::usage="";𝕖𝕕::usage="";𝕓𝕔2::usage="";𝕔2𝕕::usage="";𝕓𝕒2::usage="";𝕒𝕗𝕖::usage="";
𝕒𝕖2::usage="";𝕓5𝕔::usage="";𝕒11𝕓𝕔::usage="";𝕓4𝕔::usage="";𝕒5𝕔::usage="";𝕒𝕕2::usage="";𝕓3::usage="";𝕔b::usage="";𝕔2::usage="";𝕖2::usage="";𝕖𝕓::usage="";𝕖𝕔::usage="";𝕒𝕓𝕔2::usage="";𝕒3𝕕::usage="";𝕒𝕓𝕔4::usage="";𝕒𝕔7::usage="";𝕗𝕒::usage="";𝕗𝕓::usage="";𝕗𝕔::usage="";𝕗𝕕::usage="";𝕒𝕗2::usage="";𝕒3𝕔::usage="";𝕓7𝕔::usage="";𝕗𝕖::usage="";𝕗2::usage="";𝕒𝕓𝕔𝕔::usage="";𝕔3𝕕::usage="";
𝕕3𝕖::usage="";𝕒2𝕓::usage="";𝕒𝕔13::usage="";𝕓𝕔16::usage="";𝕕3::usage="";𝕒𝕕2𝕖::usage="";𝕒17𝕓𝕔::usage="";𝕓𝕕2::usage="";𝕓11𝕔::usage="";𝕓𝕕𝕖2::usage="";𝕔𝕕2::usage="";𝕒𝕕𝕖2::usage="";𝕓𝕕𝕕𝕖2::usage="";𝕔𝕖2::usage="";𝕕2𝕖::usage="";𝕒𝕔12::usage="";𝕒𝕓3𝕔::usage="";𝕒𝕓𝕔6::usage="";𝕒𝕕2𝕖2::usage="";
𝕒𝕗2::usage="";

Aa::"usage"="96 element random integer vector ";Bb::"usage"="96 element random integer vector ";abbr::"usage"="abbr[t_,o_:1] is used by 'dico' & 'trico' (generalised signatures) to create an abbreviation such as {12,(Subscript[4, 5]),15} in which subscripts indicate numbers of appearances of elements in a table diagonal, with the first element being real for abelian and signed for signed tables. 'dico' has another discriminant appended in cases with many tables of the same size. In the example, dico[makeProtoloop['g3207']], there are 12 occurences of the unit; 5 other elements occur 4 times (total=32), and there are 15 subgroups of 4 elements.";abbrFactors::"usage"="abbrFactors[g_indexTableQ:gLoop,p_:power2] creates an abbreviation such as {(Subscript[1, 2]),2,(Subscript[2, 1]^2),(Subscript[6, 1]^2)} for the factor structure of the indexTable determinant. In this (Q36) example there are two different linear factors, a single quadratic and two repeated quadratic factors, and two repeated sixth powers. Note that abelian groups (only) have no repeated factors. power2 is used because using the simpler pow2 sometimes errs.";
abelGrassmanQ::usage="Tests if (ab)c==(cb)a for all a,b,c in 'G'";abelianQ::usage="Tests whether Transpose[g]==g.";
addSigns::usage="used by fold to convert large indices to signed indices";
allFactorGroups::usage="allFactorGroups[gg_:gLoop,o_:0,i1_:2,i2_:49,p_:{}] finds the Factor groups (quotient groups) for all normal subgroups in the size range {i1,i2} of 'gg'. If the variable 'sg' already contains the selected subgroups (i.e. after calling subgroups) set 'o' to 1 to avoid recalculation. A list may be appended; the first matching subgroup {i1,p[[_]]} is then reported and the search ends. Widely used in id";

alph::usage="32 single characters";alternativeQ::usage="alternativeQ[g_:gLoop,o_:0] tests whether xx.y=x.xy for all x,y.z in 'g'. It reports the first error if 'o'≠0. See PMA p94, or Numbers p226.";amQ::usage="Tests if x(yx.zx)=(xy.xz)x";arcTanh::usage="arcTanh[adj_,opp_] or arcTanh[{adj_,opp_}] calculates an angle that takes account of the octant of the arguments; the angle has an imaginary part for three non-standard hyperbolae. Note that {opp,adj} is the argument order used by many mathematicians.";
asa::usage="/.asa[A_,al_] replaces {a,b,.. ϕ} by coefficients in A";
associator::usage="associator[g_:gLoop,i_,j_,k_] is the standard groupoid function, (ij)k-i(jk) ";AssociativeQ::usage="AssociativeQ([gg_:gLoop,o_] tests if (x(y z))==((x y) z) for all x,y,z in 'gg' and reports the first error if 'o'≠0.";associativeQ::usage="associativeQ([gg_:gLoop,o_] tests if (x(y z))==((x y) z) (up to a sign) for all x,y,z in 'gg' and reports the first error if 'o'≠0. Some non-associative signed tables (including Qr, Octr, Sed) are associative 'up to a sign'";

bolQ::usage="bolQ([gg_:gLoop,o_] tests the left & right Bol identities (PMA p97-8) (z.yz)x ==z(y.zx) & x(zy.z) ==(xz.y)z for all x,y,z in 'gg' and reports the error type if 'o'≠0.";ca::usage="ca[m_Integer?Positive,a_Integer] or
   ca[{m_,a_:1}] checks that GCD[m,k=Abs[a]] is 1 before creating an m×m quasigroup indexTable with first row and first column containing the 'unity' {1,2,...,m}, and with every element occurring once in each row and column (i.e. it is a sorted quasigroup or Latin Square). The result is the Cyclic group 'Cm' if 'a' is 0 or absent, the Dihedral group 'D[m/2]' if 'k'='m'-1 and the generalised Quaternion group 'Q[m]' if 'k'='m'/2-1; some other values of 'k' give compound Dihedral or Quaternion groups. Some other cases give Hamiltonian quasigroups. If 'a' is negative, non-associativity is reported. The indexTable is output.";caylindex::usage = "caylindex[gg_] converts a square symbolic table 'gg' to an indexTable on the assumption that the first row is the unity.";
cBA::usage="The (sparse) Clifford BA product, created by cTimes[A,B,1] or cT1[A,B].";cBAS::usage="The negated SparseArray Clifford BA product, created by cT1[A,B], used in cRot.";
cd::usage="cd[{gamma__:IntegerQ}] (generalized Cayley-Dickson) takes a list of none or more ±1's and recursively builds signed-tables (including P,R,C,H,O,sedenions) by the generalized Cayley-Dickson doubling procedure. See Lounesto, Clifford Algebras & Spinors, 2nd. ed., p285. The recursive process starts with 'm', the table (of size q×q) obtained by dropping the last ±1; the starting case (with no ±1's) is the C1 multiplication table {{1}}. The top-left quarter of the enlarged table repeats 'm'; the top right quarter is 'm' transposed and shifted by 'q' (using 'modqr' to give a signed index); the bottom left quarter is 'm' shifted by 'q', with all but the first column multiplied by the current ±1. The bottom right quarter is 'm' transposed with all but the first row & column multiplied by the current ±1. An extension takes any of {2, -2, 3, 3., -3, 4, 4. -4, -4.,'incantation'} in place of the first ±1, and also allows '±1.' (i.e. real) elsewhere. This generates more signed hoop algebras and lots of rubbish. ('incantation' is any string that creates a hoop.) If the last gamma is {list}, e.g. {2} or {3}, the last stage is the composition of the penultimate result with the group ca[list].
   md is a related Moufang Doubling operation.";cDimensions::usage="p+q for the active Clifford (Geometric) algebra.";

center::usage="standard group function";centre::usage="standard group function";
cFullBasis::usage="cFullBasis[letr_String:nullstring] (after cLoop[p,q]) creates {0,1,10,11,100,101,110,111} etc or (if letr = a etc) {a0,a1,a10,a11,a100,a101,a110,a111}";
cGrInv::usage="lists to speed conversion from graded to flat vectors";
c𝕀::usage="(Geometric Algebra) the PseudoScalar, the final grade in a multivector. It replaces and generalises 𝕚 in many operations, becoming anti-commutative in some algebras. Left multiplication by c𝕀 generates left-handed rotations, right multiplication by c𝕀 generates right handed rotations.";cInverse::usage="cInverse[v_] calculates the Clifford inverse of a flat, sparse or graded vector, and needs shape data from sd.";
cij::usage="cij[i,j] is a compiled calculation of a Clifford product index, allowing fast sparse vector multiplication and division of graded multivectors. lp must be preset. ijc[i,j] is the unsigned inverse function";
cLL::usage="cLL[A] is the squared length, <cT[A,A]> for grade 1 sparse arrays ";
cLoop::usage="If r=0, cLoop[p,q,r] generates Clifford Algebra CLpq, using the BitXor order. It also sets up gName, mm, cDimensions, cSparse, and lp. The gLoop (Cayley table) is created if p+q<5; the compiled cij routine is available for r=0 algebras. r=1,2,3,4,-3 create octr,octi,C3,O4,C3C3; negative r triples the algebra. If p+q<5 or p is real, the Cayley table is put in gLoop and cSparse=False. Otherwise, cij is used because gLoop would be large and sh may be unknown.";
cGrading::usage="is the list of indices in succesive grades (starting with grade 0} for the BitXor order of Clifford algebra elements.
   cGrading[[i_]] lists the indices for grade[i-1], cGrading[[{i,j}]]lists the i'th and j'th grades.";cGr::usage="cGr[M,n_:0] returns the grade[n] part of M, i.e. <M(Subscript[>, n]) in [1] cGr[M,{i,j,..}] gives a list of grades.";Cl::usage="The Clifford (Geometric) product, AB=A.B+A⋀B, created by cTimes & cT";

co::usage="co[gg_?indexTableQ,hh_?indexTableQ,a_:0] outputs the direct composition of 'g' & 'h' if 'a' is 0 or absent; some values of 'a' create indirect compositions as quasigroups or groups. If 'a' is 1 or negative, non-groupoid & non-associative tables will be reported. 'gg' (but not hh) may be a signed table. co[g_,h_,gg_,hh_,a_,o_:0,p_:0] and co[g_,gg_,hh_,a_,o_:0] (NB first parameter 'a' can be 0, but must be supplied) generate the multiple compositions by iteratively composing the inner tables using the leading parameters.";
collect::usage = "collect[%], collect[sg], or collect[] is used to count the numbers of each type of subgroup identified by subgroupTypes and stored in 'sg'";conservativeQ::usage="conservativeQ[gg_:gLoop] tests whether Det[A]Det[B]=±Det[AB], for the (possibly signed) groupoid 'gg'. Frobenius showed that associativity is a sufficient condition; a few non-associative Moufang tables are conservative. Random integer values of the elements of A & B are tested if 'gg' is signed or not associative.";cosorbit::usage="cosorbit[θ_,phaselist_:{0,1,2,3,4,5},scale_:1,meanlist_:Table[0,{24}]] creates an orbit with angle parameter θ; phaselist defines the phase of each element (with null values permitted) and the number of elements; scale is a factor that can be adjusted to obtain a unitary result; meanlist is an optional offset from zero.";
cQ::usage="Tests if (xy.y)z=x(yy.z)";cRef::usage="cRef[n,A0] reflects an array A0 of multivectors in unit vector n. No tests are made, for speed of execution.";cRefS::usage="cRefS[n,A0] reflects an array A0 of sparse vectors in unit sparse vector n. No tests are made, for speed of execution.";cRot::usage="cRot[m_,n_,A0_] rotates A0, an array of sparse vectors, using unit vectors m & n. No tests are applied, for speed of execution.";cRotate::usage="cRotate[a,b,C] rotates C in the plane a⋀b by twice the angle from a to b. It calculates ((ab)C)ba.";

centralizer::usage="standard group function";
cShape::usage="list of conserved determinant factors (sizes) using double-struck characters as loop generators.";
cSparse::usage="is set to True by cLoop if p+q>4 (or p is real, to allow table creation), so that cij is used in place of gLoop in larger Clifford calculations.";cTimes::usage="cTimes[A_,B_,o_:0] takes two vectors, converts them to sparse vectors, and uses sparse vector multiplication and output. If cSparse==True, the compiled cij value is used, rather than the signed look-up Cayley table 'gName'. Cl is set as the Geometric product. If o>1, Jordan (Jo) & Lie (Li) products are calculated. 'o' determines the output:-
0 outputs Cl,      -1 outputs -cTimes[Cl,A] (reflection),
1 outputs Cl and sets cBA,  2 outputs Jo,  3 outputs Li,
4 outputs {Jo,Li},  5 outputs {Cl, Li, Jo},
6 outputs cTimes[Cl,cInverse[A]] (Dorst's sandwich product),
anything else outputs {Cl, Li, Jo}.";
cT::usage="cT[SA,SB] Minimal cTimes[SA,SB] for use in cRots. No tests. SA & SB must be Sparse.";cT1::usage="cT1[SA,SB] Minimal cTimes[SA,SB,1] for use in cRots. No tests. SA & SB must be sparse. cBAsv is created.";
c1Toc2::usage="permutation created by isoCay";
c2Toc1::usage="permutation created by isoCay";

det::usage="det[a_?MatrixQ, r_:2, t_:Times] calculates a generalized determinant, as a list containing r components, for a (not necessarily square) matrix. Putting 'r' ={1,2,3,4,5,6} gives the {permanent, ditermanent, tritermanent, teterminant, penterminant, hexterminant}; the traditional Determinant is the signed sum of the two ditermanent terms. In effect, each element of 'a' is multiplied by a power of the sign '𝕤', with (𝕤^r)=1; the final result is a list of all the determinant-like terms with a given power of '𝕤'. The calculation is recursive via a stripped down version, 'det1', a signed row or column matrix being the base case. Short matrices are transposed to become 'long', i.e. with more columns than rows. 'det' sums all the square det's, as in the Moore-Penrose inverse.
    Replacing 't_:Times' by another binary operation creates new functions. ";
det1::usage="See det";

dic::usage="The diagonal count for a table, counting the number of 1's, the total count of other entries, and the sum of diagonal element orders. The first number is real for Abelian tables & signed for signed tables. It is unique for the majority of conservative tables. Isocay can separate the rest";

dico::usage="dico[g_:gLoop] (the generalised signature) is the 'diagonal count' i.e. the count of elements of 'g' in the table diagonal, compressed via 'abbr' (q.v.). The first entry is the number of square roots of unity, and is signed if 'g' is signed, and is real if 'g' is abelian.  An extra diagnostic is added for tables with m = 32, 48, 54, 64 or 72";
distribution::usage="included to avoid loading Combinatorica";
dsRuleExpand::usage="converts gapRels to expanded double struck format";
el2::usage="128 element names (strings) ø to 𝕒𝕓𝕔𝕕𝕖𝕗𝕘 substitution list for Clifford-like algebras. ø is the scalar, '𝕒' to '𝕘' the generators (monovectors), '𝕒𝕓' etc are bivectors, '𝕒𝕓𝕔' is a trivector, etc";
el3::usage="96 element names ø to 𝕒2𝕓𝕔𝕕𝕖𝕗";
e33::usage="72 element names ø to 𝕒2𝕓2𝕔𝕕𝕖";
el::usage="Element names chosen from el2, el3, e33 etc, set up by sd[gName], cLoop";
entropicQ::usage = "Test whether wx.yz= wy.xz. PMA p63";
fa::usage = "fa[g_?indexTableQ] maps the list of symbols 'el2' onto the indexTable 'g' unless g' is too large (more than 11×11); it returns the determinant factors, dropping any -1 multiplier. Use 'fp' for larger groups; 'fp' with 12×12 (or larger) is very slow without a lot of zero elements.";factorGroup::usage = "factorGroup[n_,gg_:gLoop] first tests whether the subgroup 'n' of 'g' is normal; 'g' must be an indexTable (default 'gLTop') and 'n' a subgroup list (as output by 'lcoset' or 'subgroups'). The factorGroup g/n (also called the quotient group) is identified";fenyvesQ::usage="fenyvesQ[gg_:gLoop,o_:0] tests whether (xy.z)x=x.(y.zx) for all x,y,z in 'gg'. See Kinyon,Sci.Math.Res,19/8/3";
findROU::usage="findROU[M_,o_:0] finds rootofunity rules rofu for any root symbol in M, omitting the last rule (which clashes with u2 etc) if o≠0";flexQ::usage="flexQ[gg_:gLoop] tests whether xy.x=x.yx for all x,y,z in 'gg'. See PMA p92.";flexibleQ::usage="flexibleQ[gg_:gLoop] tests whether ⟨x,y,z⟩=-⟨z,y,x⟩ for all x,y,z in 'gg'. ?ref lost?";fold::usage="fold[g_,fo_:{2}] finds 'cen', the center of 'g', & 'cenord', the order of elements of 'cen'. For each such element it creates 'known', the list of powers. Transpose[known] is partitioned into rj. The first instance of the specified fold orders (fo) is used to reorder 'g', and 'addsigns' converts the result into signed tables. These are output (as a list of matrices if more than 1). ";fp::usage="fp[g_?indexTableQ,list_pow2] maps 'list' onto 'g' and factorises the determinant. If necessary, 'list' is right padded with zeroes.";

fromCycles::usage="converts a cycle list to permutations";
fromdbZ::usage="fromdbZ[m_,n_] opens the latest version of G. Gerrard's database";fromdb::usage="fromdb[m_,n_,o_:0,f_:{}] calls fromdbO to open tempin from the db96 file, collects smReal, the GAP name gapName, the element name list gapel, the generator and relator lists gapGens & gapRels (used by ge to create polycyclic groups and hoops), the irreducible matrix generators irrep, & Cycles, for SmallGroup(m,n) from the database (which is based on the GAP atlas of finite groups). In a few non-polycyclic cases gapGens=={}.
   The results are converted to DS format and the tempin file is closed. If o>0, gapLoop is calculated via ge[gapGens,gapRels,o,f]; if o<0 it is calculated from Cycles. gLinv is set up as pointers to irrep inverses.";
fromSizeList::usage="fromSizeList[S_:sizeList] recovers the Cartesian vector from the set of sizes S";
fromVtoA::usage="/.fromVtoA[vec_?VectorQ,a_:el] replaces the elements of V with those of a";

gapCycles::usage="cycles for the Permutation group";
gapel::usage="e.g. {ø,𝕒,𝕓,𝕒𝕓...}. Element names translated from db96";
gapGens::usage="{2,3,2} etc. Generator list found by fromdb[m,n]. For non-Polycyclic groups it is {}";
gapInverse::usage="gapInverse[V] is Vector Inverse after fromdb[m,n]";gapInv::usage="gapInv[i,j] is irrep[i,GLinv[j]], i.e. the inverse of irrep[i,j]. gapInv[M] is a matrix inverse, used in gapInverse";
gapLoop::usage="Cayley Table from db[m,n,1]";gapName::usage="C3C3, C4iC3 etc. Group name simplified from that used in GAP, found by fromdb[m,n]. Indirect compositions are often ambiguous ";
gapPerm::usage="Permutation group set up by fromdb[mm,nn,-1]";gapRels::usage="{ba->aab} etc. Relator rules found by fromdb[m,n]. If gapGens={},gapRels is a list of permutations that define the (non-polycyclic) group";gapShape::usage="If irrep has been set via fromdb[m,n], gapShape[V_?VectorQ,o_:0] calculates the sizes of vector V as matrices involving s, the r'th root of unity, and then multiplies and simplifies them to Reals via the smReal lists. The unprocessed sizes are stored as sizeList.";
gapTimes::usage="gapTimes[vA,vB,g_:gapLoop] is a minimal demonstration of Cayley multiplication of two vectors vA,vB using a square table g of the same length. Remainders are not generated. Default table is gapLoop, not gLoop";

gd::usage="gd[] returns {mm,nn,{loop entry}} for the last loop to be identified.
   gd[Mnemonic_],gd[m_,n_] or gd[{m_,n_}] returns the requested 'loop' data";
ge::usage = "ge[gp0_,pre_,o_:0,f_:{}] creates quasigroups via 'relators' and 're-write rules'. The 'relators' are symbols {𝕒, 𝕓, ..} that concatenate to lex-ordered elements such as 𝕒2𝕓𝕔2; the symbol ø is the neutral element. The re-write rules define any non-Abelian re-orderings, eg 𝕓𝕒->𝕒2𝕓. gp0 is usually a flat list of generator lengths. E.g.{5,4,2.} implies 𝕒𝕒𝕒𝕒𝕒->ø, 𝕓𝕓𝕓𝕓->ø, 𝕔𝕔->ø and the real '2.' for 𝕔 implies that the table can be folded on this generator if the fold parameter f contains index 3.
   Clifford-like algebras are described by a non-flat list e.g. {{2,2,-2},2} implies that 𝕒, 𝕓 & 𝕔 anticommute, 𝕒𝕒->ø, 𝕓𝕓->ø and 𝕔𝕔->𝕕 (~-1). Clifford data is used first, and then suppressed by gpa=Flatten[Abs[gp0]].
   If 'gp' is {na, nb,...}, 'ge' sets up a vector of ordered elements starting with ø, followed by up to 'na'-1 repetitions of 𝕒, followed by 'nb'-1 repetitions of 𝕓, etc but not beyond 𝕘. (i.e. only 7 generators are allowed.) 'pre' contains any re-write rules for out-of-order letters. Bad rules (with wrong characters, overlong character repeats, etc) are rejected if 'o'>=0.
   A full set of re-write rules is created from 'pre' by adding any unspecified Abelian rules such as 𝕓𝕒→𝕒𝕓. A preliminary array is created by concatenating the elements. The re-write rules are then applied to reduce concatenations to ordered names.
   If Abs[o]=1, non-quasigroups are rejected, non-conservativity is reported, the table is put into  list 'matel', and the elements are put into  list 'gel'. The reduced array is converted to an indexTable g.
   Folded Hoops. These are obtained if f={n_}, where n is a list of foldable indices. Or if gp0 includes {integer} as the last element, the output will be folded on this generator. 
   In db data the last few elements of gp may be real numbers 'r.' representing cyclic central subgroups, and g can be folded to a signed table by g=ts[g,r]. The 'f' list (default {}) contains the indices to fold over.
   Finally, g is output.
   String processing is used. maxel and gel are created using strings but ToExpression is applied.";gel::usage="The elements of the last generator group to have been created with 'o'=1";

gi::usage="Data required by hoopInverse & set up by cLoop, sd, or shape, consisting of the location of the signed 1's in the indexTable rows, multiplied by the inverse sign if the 1 is signed, & followed by the multiplicity of the factors (which is zero for factored quartics).";gInverse::usage="finds the element inverses";gLinv::usage="gLoop element inverses, after fromdb[m,n,±1], used in gapInverse.";gLoop::usage="Set by 'cLoop', 'ge', 'ma', 'pe', 'hoopTimes', 'makeProtoloop' (fromdb[m,n,±1] sets gapLoop) as the indexTable of the (active) loop being created or investigated. It is the default argument in many operations. 'cij[i,j] is a compiled routine to calculate gLoop[[i,j]].
   (fromdb[m,n,±1] creates gapLoop, not gLoop). See 'cLoop', 'gLTop', 'gName'.";gLTop::usage="Set by 'subgroups'. The indexTable of the (top)  loop being analyzed. See 'gLoop', gName'";

gmap::usage = "gmap[gg_,v_] maps the elements of the list 'v' onto the indexTable 'g', which may include signed elements.";gName::usage = "Set by 'cLoop', 'id' & 'makeProtoloop'; the mnemonic for the current (active) loop, used widely as a default argument. See 'gLTop', gLoop'";gp::usage="Size multiplicity data needed by 'hoopPower', set up for the target loop by 'sh', & 'toPolar'";gpd::usage="gpd[gg_] is used on function arguments that should be groupoids (i.e. magmas, loops, quasigroups). It removes any TraditionalForm wrapper and rejects non-groupoids by 'Abort[]'. The first row must contain the elements, which may be matrices; signed elements are permitted in the body of the table.";

hamiltonianQ::usage="hamiltonianQ[g_:gLoop] is true if 'g' is not abelian but all subgroups are normal";hmin::usage="hmin is arbitrarily set at 4$MachineEpsilon as the criterion for 'hoopInverse' to ignore (renormalize) partial fractions with near-zero denominators.";
hoopInverse::usage="hoopInverse[vec_?VectorQ] finds the multiplicative left inverse of 'vec' (vec is right-padded with zeroes if necessary) in the algebra specified by 'gLoop'. It is effective provided that the algebra is conservative - i.e. the determinant of the product is the product of the multiplicand determinants (up to a sign). The procedure is related to Cramer's method. If the symbolic determinant factorises, the inverse splits into partial fractions with determinant factors as denominators and their derivations as numerators. The sequence of derivation variables is fixed by the location of 1's in the IndexTable, and is given in 'gi'.
   'Partial-fraction division-by-zero' (renormalisation) is implemented by omitting partial-fractions with denominators (sizes) that are within ±'hmin' of zero. 'hmin' has been arbitrarily set at 4$MachineEpsilon (=2.^-50 on my machine). Renormalisation corresponds to projecting any vec onto a constrained sub-algebra whilst 'ejecting' remainders Rl, Rr to maintain conservation if needed.
   cInverse handles flat or graded vectors in Clifford algebras. See also cInverse, gapInverse";
hoopList::usage="List of hoop names";hoopPower::usage="hoopPower[A_, r_:1/2] calculates (A^r) if the target loop has a polar form.";hoopRoot::usage="hoopRoot[A_?VectorQ] calculates the square root of A in the target algebra if it has a polar form. It is faster than using hoopPower.";hoopTimes::usage = "hoopTimes[a,b] or hoopTimes[a_,b_,gg_:gLoop] multiplies the vectors 'a' & 'b' to give a product 'p' according to the indexTable 'gg'. This may include signs. Remainders Rl & Rr are created, so that a=p/b+Rl, b=p/a+Rr, maintaining conservation. cTimes handles flat or graded vectors in Clifford algebras. cT and cT1 are fast versions.";id::usage = "id[G_,L_:{}] uses a range of tests to identify 'G', which may be a name, or {mm,nn}, or an indexTable; if an index-list 'L' is specified, the corresponding subgroup of 'G' is identified. Associativity is not tested (for speed of execution) so unknown groupoids may be wrongly identified. Names: Cn, Dn/2, & Qn are cyclic or generalised Dihedral and Quaternion groups with n elements. An & Sn have n generators. Alt12n, Oct, D4Mn etc  are 'Square associative' or 'alternative aa.b=a.ab' groupoids. XY, XiY,XpY are the direct or indirect compositions of X & Y. Xa is a second isomorph of X. Xr & Xc are conservative signed tables, obtained by folding X, that also provide conservative algebras on expanding with C2 or (C2 & C4). Loops with names ending in n are not conservative. Loops with M in the name are non-associative Moufang loops. gnnmm is GAP SmallGroups(mm,nn). If the name contains ? identification is provisional because all groups of that size have not been distinguished. The variables gLoop, gName, mm,& nn are set by id. gName is returned and gd[] will provide more details.";idc::usage = "idc[G_?MatrixQ,L_:{}] checks that 'G' is conservative before attempting identification via 'id'";ijc::usage="ij[ci,j]] is the unsigned inverse of cij[i,j]";indexTableQ::usage="indexTableQ[gg_:gLoop]] checks that the first row and column are Range[Length[gg]] and that every row and column contains each of these (possibly signed) integers once";
im::usage="Length of irrep, set by fromdb";irreplen::usage="smatrix lengths, set by fromdb";irrepReal::usage="The list of sets of irrep elements that combine to give a real size";
isoCay::usage="isoCay[g1,g2] puts g1 & g2 into global arrays cay1 & cay2 and initialises global itn and permutations i1 &12. It calls (recursive) isoCay[], which seeks the permutations that match cay1 with cay2. On succeeeding it returns True and sets c1Toc2 and c2Toc1 as the permutations that convert one array (and related vectors) into the other isomorph.";

jacobiQ::usage="jacobiQ[gg_:gLoop,o_:0] tests whether xy=-yx & x.yz+y.zx+z.xy=0 for all x,y,z in gLoop";jm::usage="2nd. Length of irrep, set by fromdb";Jo::usage="The Jordan product, A.B, created by cTimes"; 
jordanQ::usage="jordanQ[gg_:gLoop,o_:0] tests whether (xy).xx=x(y.xx) up to a sign";KS::"usage"="KS[l_List,k_Integer?Positive,gap_:{},lef_:{}] is an adaptation of k-subsets in Skiena p44, to create subsets, of length 'k' of group indices that give groupoids from 'gLTop'. It creates a list 'gap' of rejected indices and a list 'lef' of elements left in, adding to 'lef' those new elements that do not have any products in 'gap'.";

lcoset::usage = "lcoset[h_,g_:gLoop] finds the left coset for the subgrouplist 'h' in the indexTable 'g' or in 'gLoop'";Li::usage="The Lie product, A⋀B, created by cTimes"; lmatrix::usage = "lmatrix[gg_?indexTableQ] converts 'gg' into the corresponding matrix with 1's on the diagonal and {1,2,3..,m} in the first column. If an ordered set of symbols or numbers is mapped onto an lmatrix, the groupoid product is given by the left matrix dot product of this matrix and any other ordered set. Cf rmatrix.";
lp::usage="2^p, the number of positive generators in the active Clifford Algebra";

loop::"usage"="loop[[mm,nn]] is the original data file. 'mm' is the number of elements, and 'nn' is the position in the extended GAP Atlas entry. For each loop, the first entry is the mnemonic, the second is the identifier 'dico', the third specifies an identification test (0 if 'dico' is unique), the fourth is a prescription, the 5th & 6th define the generators. If matrix formulations are known they are supplied as indices for 2\[Cross]2, 3\[Cross]3, & 4\[Cross]4 standard matrices u2, u3, u4. In a few cases, extra table creation procedures are appended. A tenth entry may contain a list of generating cycles.";
loopQ::usage="loopQ[gg_?MatrixQ,o_:0] tests whether the first row and first column are the same set of different elements (i.e. are the unit) and every row and column contain every element once (up to a sign). If 'o' ≠ 0 the reason for rejection is output. PMA p87";

ma::"usage"="ma[{mm__},maxel_:80,o_:0] takes a list of one or more unitary monomial signed square matrices (all of the same size) and prepends the unit matrix. It then creates the dot products of these matrices and appends any that are not already present, until the size exceeds 'maxel' or a group has been completed. The group is then created as the element list 'matel' which is output if o≠0; the indexTable is put into 'gLoop' and is output.";matel::usage="The elements of the latest matrix (ma or ms) or relator (ge) group. (The last relator acts as a sign in a signed table.)";makeProtoloop::usage ="makeProtoloop[g_:{mm,nn},o_:0] is the full name for 'mp'. makeProtoloop[] or makeProtoloop[mm,nn] uses the first available prescription in gd[mm,nn] to create the protoloop.
   makeProtoloop[G_:MatrixQ,o_:0] recognises three formats for G - a string (mnemonic) as a name, indices {mm,nn} in 'loop' (i.e. the extended GAP Atlas identifiers), or a matrix. It then attempts to make the protoloop, returning 'Unknown' or 'No protoloop' and clearing matel as appropriate. If 'o'=0 it uses the first available formulation. If 'o' is 1, 'ge' is used.  If 'o' is 2, 3, or 4, the corresponding matrix formulation is used in mg. ms is used for signed tables.
   If 'o' is 5 or 6, different protoloops may be generated (only P16a, P16i, g2003, Alt12n so far). The indexTable is output.";

matstrep::usage = "matstrep[l_,rul_,sm_:smax] performs up to 'sm' string replace repetitions on the matrix.";md::usage="md[g_,l_:{}] (Moufang doubling) creates a non-associative Moufang loop from a non-abelian group. l={} uses gInverse to implement Chein doubling; 3 cases use l as a reordering.";mg::usage="mg[v_?VectorQ,u_,maxel_:80] (Matrix Group) creates a loop by sending the u matrices indexed in 'v' to 'ma'. u may be u2, u3, or u4. The indices may be signed; the sign is applied to the matrix. The collections of 'unitary monomial matrices' in u2, u3, and u4 are arbitrary; they need rationalising and the lists of their indices in loop should be reconstructed and extended.";
minSign::usage="minSign[g_] finds any signed elements in 'g' and sets up the appropriate simplification list from 'sr'";mm::usage="mm is the length of the active loop 'loop[[mm,nn]]', set by 'id' & 'gd', used as {mm,nn} in many procedures";modqr::usage="The 'modqr' function shifts a signed index 'r' by 'q' whilst keeping in the range ±{1,2q}. e.g. modqr[3,-2] = -5. Used in 'cd'.";MoufangQ::usage="MoufangQ tests if zx.yz=(z.xy)z, the 3rd Moufang Identity. See PMA p92. As this fails for many conservative signed tables such as Qr, unsigned tests can be performed by moufangQ.";moufangQ::usage="Tests if |zx.yz|=|(z.xy)z|, the (unsigned) 3rd Moufang Identity. See PMA p92";mp::usage="mp[] or mp[mm,nn] uses the first available prescription in gd[mm,nn] to create the protoloop.
   mp[G_:MatrixQ,o_:0] recognises three G formats - a string (mnemonic) as a name, indices {mm,nn} in 'loop' (i.e. the extended GAP Atlas identifiers), or a matrix. It then attempts to make the protoloop, returning 'Unknown' or 'No protoloop' and clearing matel as appropriate. If 'o'=0 it uses the first available formulation. If 'o' is 1, 'ge' is used.  If 'o' is 2, 3, or 4, the corresponding matrix formulation is used in mg. ms is used for signed tables.
   If 'o' is 5 or 6, different protoloops may be generated. (Permutation incantations are lists with o=5.) The indexTable is output.";

ms::usage="ms[v__?ListQ,l_:u2,maxel_:80] makes signed tables that may be hoops, from the specified unitary monomial matrices. It puts the unit matrix and either the matrices in v (or if v is a list of indices, possibly signed, the listed matrices from l, where l is u2, u3, or u4), into matel. It then creates a table from their dot products, adding any that do not match signed existing elements, up to a limit maxel. ms is used in place of mg in mp for signed tables";msi::usage="msi[v__?ListQ,l_:u2,si={1,-1,I,-I},maxel_:64] is a variation on ms that handles P4 and P16c";mstst::usage="mstst[m_,s_] tests whether matel contains a version of the matrix m, multiplied by the signs in s, returning 0 or the corresponding sign for use in ms.";

nabco::usage="count of diagonal 1's";
negco::usage="count of diagonal -1's";
negatableQ::usage="negatableQ[gg_:gLoop,f_:2] tests whether the table 'gg' has the same elements in each 1/f × 1/f fraction with elements shifted by 'm/f' (allowing for signs). If so, the top left fraction may describe a conservative signedTable.";nn::usage="'nn' is set by 'id', 'hoopTimes & 'gd', and used in {mm,nn} to identify the position of an entry (of length mm) in 'loop'";normalSubgroup::usage = "normalSubgroup[h,g] tests whether 'h' is a normal subgroup of 'G', i.e. gh(OverBar[g])ϵH, all g,h.";o::usage="used as a control parameter in many functions, +/-/real/Integer often give different results.";orderCount::usage="gives the order of each element in 'g'";pe::usage="Generates a loop from a list of permutations such as s4";
period::usage="standard group function";
permFromQ::usage ="tests if a valid permutation";
permute::usage="If 'p' is a valid sub-permutation, permute[P_List,p_List] returns the sublist of 'P'";
pgcd::usage="pgcd[p_] reduces a polynomial in s (where s^𝕣=1) as the GCD with Cyclotomic[𝕣,s]. Used to convert suitable irrep products to real sizes.";
pick::usage="pick[g_,m_List,n_List] picks out the rows 'm' & columns 'n' from 'g'";pow2::usage="A list {ø,1,2,4,8..} used as elements of Cayley Tables to allow fast determinant evaluation via fp & 'linearFactor'. (May have problems with some Clifford algebras - use fp[G,power2 or power3].)";power2::usage="A list {ø,3,7,1,2,4,8..} used as elements of Cayley Tables to allow fast determinant evaluation via 'fp'";
pr::usage="Diagnostic output control";
proto::usage"proto[L,v] Converts loop v to the protoloop, with elements in reducing prime order, and reorders the vector v to match.";
prs::usage="prs[p_]:=Ep,Cyclotomic[𝕣,s],s] simplifies a polynomial in s, where s^r=1.";

𝕣::usage="exponent in roots of unity 𝕤^𝕣=1";rcoset::usage = "rcoset[h_,g_] finds the right coset for the subgrouplist 'h' in the indexTable'g' or in 'gLoop'";reductiveQ::usage="tests xy.xx=x(y.xx)";reorder::usage = "reorder[gg_?indexTableQ,p_] generates the indexTable of 'gg' as reordered by the permutation 'p'; short permutations give sub-tables.";
riffQ::usage="Tests if xy(z.xy)=((x.yz).x)y";
rofu::usage = "roots of unity conversion rules. Initially {}, extended by findROU in sd, ma etc, fromdb.";
rs3::usage="1/Sqrt[3], used in some sizes";Rl::usage="The left remainder from the last P=hoopTimes[A,B], a vector containing the sizes of A that are zero in P";Rr::usage="The right remainder from the last P=hoopTimes[A,B], a vector containing the sizes of B that are zero in P";rmatrix::usage = "rmatrix[gg_?indexTableQ] converts 'gg' into the corresponding matrix with 1's on the diagonal and {1,2,3..,m) in the first row. If an ordered set of symbols or numbers is mapped onto an rmatrix, the groupoid product is given by the right matrix dot product of this matrix and any other ordered set. Cf lmatrix";
rU::usage="implements double-struck roots of unity";
ruleExpand::usage = "ruleExpand[a] applies 'stringExpand' to a list of compressed rules e.g 𝕒4𝕓2→𝕒𝕒𝕒𝕒𝕓𝕓.";
rus::usage="implements additive elimination for roots of unity";

s::usage="root of unity in irrep";sd::usage="sd[] clears, sd[g:gName] sets size data (el;rofu;gi;gp;sh).";
select::usage="select[l_] finds all elements appearing as products in the subarray 'l' of 'gLTop'";
s3::usage="s3 is the list of permutations that define S3";s4::usage="s4 is the list of permutations that define S4";s5::usage="s5 is the list of permutations that define S5";sg::usage="sg is the () list of subgroup indices created by 'subgroups'; used by 'subgroupTypes'";sh::usage="sh lists the symbolic factors of the active symbolic hoop determinant after sd[gName].";shape::usage="shape[a_VectorQ,mnemonic_,g_:gName] obtains specific shape data (where known) from sd for the specified loop (default: gName). The conserved determinant factors are supplied, and the lists el, gi & gp are set up for use by hoopInverse & toPolar.
   shape[a_] uses a=tocFlat[a], for the active loop.";sgroup::usage = "sgroup[m_?IntegerQ] is adapted from Skiena p17. It creates the indexTable for S[n]";sh12::usage="sh12[{12vec}] is the standard shape data for Dozal, the 12-element groups C3C4, C3K, Q12, D3C2, A4. It includes functions that are conserved on general multiplication but are not determinant factors, and others that are only conserved in some multiplications of orbits";

signList::usage="signList={𝕟,𝕠,𝕧,𝕙,𝕡,𝕏,𝕐,𝕁,𝕜,𝕞} is the list of extended signs. These are different 9th, 8th, 7th, 6th, 5th, 4th, 3rd, 3rd, 2nd & 2nd roots of +1 respectively. Related symbols:- 𝕒 to 𝕘 are generators. 𝕤 is the general sign or 𝕣'th root of +1. c𝕀 is the PseudoScalar of any Clifford algebra, with ((c𝕀)^2)=±1 depending on the signature.";
𝕙::usage="Extended Sign. (𝕙^6)=1";𝕁::usage="Extended Sign. (𝕁^3)=1";𝕜::usage="Extended Sign. (𝕜^2)=1";𝕞::usage="Extended Sign. (𝕞^2)=1";𝕟::usage="Extended Sign. (𝕟^9)=1";𝕠::usage="Extended Sign. (𝕠^8)=1";𝕡::usage="Extended Sign. (𝕡^5)=1";𝕧::usage="Extended Sign. (𝕧^7)=1";𝕤::usage="Generalised Extended Sign, the 𝕣'th root of unity. \!(𝕤^𝕣)=1";(*s::usage="Generalised Extended Sign in db1, the 𝕣'th root of unity. (s^𝕣)=1";*)
𝕏::usage="Extended Sign. (𝕏^4)=1.";𝕐::usage="Extended Sign. (𝕐^3)=1.";

signedTableQ::usage="tests whether the group is an indexTable with signed elements.";
sizeList::usage="The raw s-polynomial sizes created by gapShape";
irrep::usage="Irreducible affording matrices (See the GAP manual!) collected from GG's 25MB databse by fromdb[m,n]";
strep::usage = "created by ge[...,±1] as string replacement rules.";streprpt::usage = "streprpt[str_,rul_,imax_] performs up to 'imax' string replace repetitions using the list 'rul'.";stringExpand::usage = "stringExpand[t] replaces 'letter integer' by 'integer' repetitions of 'letter' in the string 't'.";

subgroupTypes::usage = "subgroupTypes[] or subgroupTypes[%] may be used after subgroups[g] to identify them in order."; subgrpPerm::usage="subgrpPerm[G_,a_:0] & subgrpPerm[G_,a_,b_,c_] are implementations of RandomPermutation from Skiena p7. They permute the group to increase the chance of pruning, and usually speed up the determination of subgroups for groups with 'm'>47. a, b, & c are arguments that are passed through.";subgroups::usage = "subgroups[g_,o_,i1_,i2_,p_:associativeQ] finds all the subloops, in the IndexTable 'g' that pass the 'p' test, so the default finds subgroups, within the optional length range {i1,i2}, as sublists of indices. 'gLTop' is set to 'g'. If 'o'=0, the number of subloops is output; if 'o'=1 the sublist is put into 'sg', for use by 'id' and is output; o=2 gives both.
  subgroups[g_,-n,i1_] or subgroups[g_,any,i1_,any,{n__}] test whether the subgroup identified as {i1,n} or {i1,n__} is a subgroup of 'g', returning 0 or the first matching n__ found. Used by 'id'";
tf::usage="TraditionalForm";
tidy::usage = "tidy[g_:gLTop,n_:-1,o_:1,p_:{}] uses the list 'n' (or the n'th subgroup if 'n' is an integer; the default is the last found subgroup) in the top-left corner of a reordering of 'g'; 'o' is the (optional) element at the beginning  of the next column. 'p' is the (optional) starting  element (or list) for the remainder. The reorder list and the new table are output. The default group is 'gLTop', as set up by 'subgroups'. It is faster to specify a subgroup as an element-list than to specify a position in the subgroup list, as the latter has to proceed via 'subgroups', which is slow for large groups";

tocFlat::usage="tocFlat[A] converts a graded or sparse vector to a flat list, right-padded with zeroes to length mm.";
tocGr::usage="tocGr[A] converts a flat list to a graded list
   tocGr[A,gr] picks out the specified grade, implementing <A(Subscript[>, gr]).";
tocSparse::usage="Sparsifies a flat or graded vector to a matrix of indices and non-zero coefficients. Sparse matrices are unchanged.";
toCycles::"usage"="toCycles[perm_?VectorQ] generates the cycles from the permutation.";
toDs::"usage"="converts 0abcdefg to doublestruck";tohyPol::usage="tohyPol[{radius,angle}__,mnemonic_] contains the hyperbolic forms for Abelian hoops";tohyPolar::usage="tohyPolar[vec_,mnemonic_] obtains the hyperbolic form for the current Abelian groupoid";tohyVec::usage="tohyVec[{ulna,angle}__,mnemonic_] contains the hyperbolic forms";tohyVector::usage="tohyVector[hpf_,mnemonic_] reverts the hyperbolic form for the current groupoid";
toPol::usage="toPol[vec_,mnemonic_] gives the polar form of vec in the specified hoop.";toPolar::usage="toPolar[vec_,mnemonic_] obtains the polar form from the vector form for the current groupoid";toSignedTable::usage = "toSignedTable[g_?MatrixQ,r_:2,reo_:{},o_:0] (abbreviation ts) attempts to collapse 'g' to a well-ordered signed table of length m/|r|, reordering if 'reo' is provided. Non-conservative tables are rejected unless 'r'<0.";
toVec::usage="toVec[mnemonic_] gives the vector form, using 'el2' variables.";

trico::usage="trico[g_] is the count of elements of 'g' having cube roots, with the unit roots first ";ts::usage = "ts[a___] is an abbreviation, used in data, for toSignedTable[g_?MatrixQ,r_:2,reo_:{},o_:0]. It attempts to collapse 'g' to a signed table of length m/|r|, after reordering if 'reo' is provided. Non-conservative tables are rejected unless 'r'<0.";u2::usage="u2, u3 & u4 are lists of 2×2, 3×3 & 4\[Cross]4 monomial unit matrices that include the Pauli Sigma and Dirac Gamma and Tau matrices. These allow development of matrix groups with different symmetries. Only some root matrices are included; dot multiplying them together generates many more. In combination with 'loop' & 'makeProtoloop', they allow the generation of many small groups with sets of matrices as elements. Further work is needed to increase the number of groups handled.";u3::usage="See u2";u4::usage="See u2";union::usage="Finds the unsorted union. Same as UnionNoSort of EAAM";
unsign::usage="unsign[g] replaces negated or complex signed elements in 'g' by the indices of the expanded table.";
ω::usage="ω=2π/3 used in many orbits";

8.3 Usage for Predefined Index & Signed Tables.

(*2,3 elements *)
C2::usage="indexTable for C2";C3::usage="indexTable for C3";C3n::usage="indexTable for signed non-associative C3n";
C3C4r::usage="conservative I-signedTable";C12c::usage="conservative I-signedTable";
(* 4 elements *)
C4::usage="indexTable for C4";C2C2::usage="indexTable for C2C2";P4::usage="complexTable from P16 ≡ Pauli algebra";P16c::usage="complexTable from P16";C4C3c::usage="signedTable from C4C3";Q4n::usage="non-conservative signedTable related to Q4 & P4";
(* 5 elements *)
C5::usage="indexTable for C5";C5n::usage="The smallest non-associative Jacobi-identity loop (arXiv:hep-th/0111292 v1)";
(*6 elements *)
C6::usage="indexTable for C6=C3C2";S3::usage="indexTable for D6=S3";D6C2c::usage="signed indexTable from D6C2";C6n::usage="A loop with the repeated quadratic size of S3 replaced by two signed sums of 6 squares. Passes the hamiltonian test (only)";

(* 8 elements *)
C4C2::usage="indexTable for C4C2";C8::usage="indexTable for C8";C2C2C2::usage="indexTable for (C2^3)";D8::usage="indexTable for D8";Q8::usage="indexTable for quaternion group";CL12::usage="signedTable Clifford(1,2)";P8::usage="signedTable from C2C2C2C2";
Octi::usage="'splitOctonion' signedTable from M(16,2)";Octr::usage="signedTable from Oct or M(16,3)";O4::usage="signedTable from C4C2C2; O4a & O4b are isomorphs.";O4k::usage="A signedTable from C4C2C2 with 4 linear and two quadratic sizes.";Q8C2r::usage="signedTable from Q8C2";

(* 9 elements *)
C3C3::usage="indexTable for C3C3";

(* 12 elements *)
C12::usage="indexTable for C12=C3C4";C3C2C2::usage="indexTable for C3C2C2";Q12::usage="indexTable for Q12";A4::usage="indexTable for A4";D12::usage="indexTable for A4";C2C2S3::usage="indexTable for C2C2S3=D6C2";C3P4::usage="conservative 12-element complexTable";

(* 16 elements *)
Q16::usage="indexTable for Q16";D8C2::usage="indexTable for D8C2";C4C4::usage="indexTable for C4C4";Q8C2::usage="indexTable for Q8C2";
C8yC2::usage="indexTable for C8:C2";C2C2C2C2::usage="indexTable for KK ≡ (C2^4)";C4C2C2::usage="indexTable for C4C2C2";C2C2;C4::usage="indexTable for C2C2:C4";C4yC4::usage="indexTable for C4:C4";P16::usage="indexTable for Pauli group P16";P16a::usage="second indexTable for Pauli group P16";P16i::usage="third indexTable for Pauli group P16";Oct::usage="conservative alternative 16-element indexTable";CL4::usage="16 element signedTable from g3250";Q8M::usage="indexTable for 16-element associative Moufang Loop from Q8, GAP M1602";

(* 21+ elements *)
g2101::usage="C3:C7";SL23::usage="indexTable for 24-element group SL[2,3]";OctrC3::usage="conservative alternative 24-element signedTable";P27::usage="indexTable for group P27, g2703";g2704::usage="indexTable for 27-element group C9iC3 without prescription";
OctC2::usage="";
OctC2M::usage="conservative alternative 32-element indexTable, GAP M3216";P16M::usage="indexTable for 32-element non-associative Moufang Loop from P16, GAP M3221";C8pC2M::usage="indexTable for 32-element non-associative Moufang Loop from C8pC2, GAP M3235";KiC4M::usage="indexTable for 32-element non-associative Moufang Loop from C2C2C4, GAP M3254";C4iC4M::usage="indexTable for 32-element non-associative Moufang Loop from C4iC4, GAP M4365";OctC3::usage="conservative alternative 48-element indexTable";

9. Start Private definitions.  Create Hoop Database.

9.1 Begin Private.

Begin["`Private`"];

9.2 Miscellaneous definitions Aa, Bb, alph, asa, arcTanh, det, el2, el3, e33, hmin, pick, pos, unsign etc.

Aa={-1,2,-2,-1,2,0,1,3,1,1,3,-1,1,3,0,-1,0,2,3,-1,-2,1,-1,-1,0,3,2,2,-2,-2,-1,2,2,-1,1,-2,2,1,-1,-1,0,0,-2,-2,1,3,-2,-1,3,3,-1,2,2,0,3,-2,3,-2,-1,1,3,0,3,3,2,3,3,0,2,3,0,-2,3,-1,3,3,3,-1,3,-2,-2,-1,-2,2,-2,3,3,-2,1,-1,-1,-2,2,-2,2,0};
Bb={2,-1,2,1,2,3,-2,3,-2,1,0,0,-2,-1,-1,3,1,0,0,-1,3,1,-2,-2,1,3,-1,-2,1,2,-1,1,2,3,-1,-1,-1,-1,0,3,2,2,3,1,-2,-2,2,-1,2,2,0,-2,-1,-2,2,0,2,1,0,0,2,-2,3,3,-1,-2,0,2,-1,2,1,3,0,0,3,-1,2,-1,1,-1,3,0,0,1,1,3,-2,1,-1,2,3,2,2,1,-1,-1};
alph={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,α,β,χ,δ,ϵ,ϕ};
asa[A_,al_:alph]:=Table[Rule[al[[i]],A[[i]]],{i,Min[Length[A],32]}]

arcTanh[adj_,opp_]:=Module[{x=Chop[adj],y=Chop[opp],b},If[(x==y||x==-y),If[x≠0,∞ Sign[y]/Sign[ x],0,0],b=Log[(x+y)/(Sqrt[(x^2)-(y^2)])//N];Chop[Re[b]+I Chop[Im[b]]]]];arcTanh[{x_,y_}]:=arcTanh[x,y];

det[(a_)?MatrixQ,r_:2,t_:Times]:=Module[{b=a,c,d,ln=Length[a],lm=Length[a[[1]]],𝕤},
Which[ln==1,d=Sum[𝕤^(ii-1)*a[[1,ii]],{ii,lm}],
           lm==1,d=Sum[𝕤^(ii-1)*a[[ii,1]],{ii,ln}],
           True,If[ln>lm,b=Transpose[a];lm=ln];
c=𝕤*b[[1]];
b=Transpose[Drop[b,1]];
d=Sum[If[c[[ii]]===0,0, 𝕤^ii* t[c[[ii]],det1[Drop[b,{ii}],𝕤,t]]
       ],{ii,lm}]];
CoefficientList[Expand[d]//.{𝕤^any_->𝕤^Mod[any,r]},𝕤]/.𝕤->Switch[r,1,1,2,-1,3,𝕁,4,I,5,𝕡]];
det1[a_,𝕤_,t_]:=Module[{ln=Length[a],lm=Length[a[[1]]],b,c},If[lm==1,Sum[𝕤^(ii-1)*a[[ii,1]],{ii,ln}],b=Transpose[a];c=𝕤*b[[1]];b=Transpose[Drop[b,1]];Sum[If[c[[ii]]===0,0,𝕤^ii*t[c[[ii]],det1[Drop[b,{ii}],𝕤,t]]
  ],{ii,ln}]]];

distribution[l_List]:=distribution[l,Union[l]];(* From Skiena p106 *)
distribution[l_List,set_List]:=Map[(Count)[l,#]&,set];select[l_?ListQ] :=Union[Flatten[Table[gLTop[[l[[i]],l[[j]]]], {i, Length[l]}, {j, Length[l]}]]];union[lst_]:=(* Union No Sort as in EEAM. Available as UnsortedUnion in Functions*)
Apply[Head[lst],Fold[If[MemberQ[#1,#2],#1,Append[#1,#2]]&,{First[lst]},Drop[lst,1]]]

permFromQ[p_List,n_Integer]:=Length[Complement[p,Range[n]]]==0&&Sort[p]==Union[p];permute[P_List,p_List]:=If[permFromQ[p,Length[P]],P[[p]],Print[{P,p," error"}]];toCycles[perm_?VectorQ]:=Module[{c,i,m,n,p=perm},If[Sort[p]==Range[Max[p]],Select[Table[m=n=p[[i]];c={};While[p[[n]]≠0,AppendTo[c,m=n];n=p[[n]];p[[m]]=0];c,{i,Length[p]}],#1=!={}&],"Not a Permutation"]];fromCycles[cyc_List]:=Module[{p=Range[Max[Flatten[cyc]]],pos},Scan[(pos=Last[#1];Scan[Function[c,pos=p[[pos]]=c],#1])&,cyc];p];tf=TraditionalForm;rs3=1/Sqrt[3];
hmin=4$MachineEpsilon;

el2={ø,𝕒,𝕓,𝕒𝕓,𝕔,𝕒𝕔,𝕓𝕔,𝕒𝕓𝕔,𝕕,𝕒𝕕,𝕓𝕕,𝕒𝕓𝕕,𝕔𝕕,𝕒𝕔𝕕,𝕓𝕔𝕕,𝕒𝕓𝕔𝕕,𝕖,𝕒𝕖,𝕓𝕖,𝕒𝕓𝕖,𝕔𝕖,𝕒𝕔𝕖,𝕓𝕔𝕖,𝕒𝕓𝕔𝕖,𝕕𝕖,𝕒𝕕𝕖,𝕓𝕕𝕖,𝕒𝕓𝕕𝕖,𝕔𝕕𝕖,𝕒𝕔𝕕𝕖,𝕓𝕔𝕕𝕖,𝕒𝕓𝕔𝕕𝕖,𝕗,𝕒𝕗,𝕓𝕗,𝕒𝕓𝕗,𝕔𝕗,𝕒𝕔𝕗,𝕓𝕔𝕗,𝕒𝕓𝕔𝕗,𝕕𝕗,𝕒𝕕𝕗,𝕓𝕕𝕗,𝕒𝕓𝕕𝕗,𝕔𝕕𝕗,𝕒𝕔𝕕𝕗,𝕓𝕔𝕕𝕗,𝕒𝕓𝕔𝕕𝕗,𝕖𝕗,𝕒𝕖𝕗,𝕓𝕖𝕗,𝕒𝕓𝕖𝕗,𝕔𝕖𝕗,𝕒𝕔𝕖𝕗,𝕓𝕔𝕖𝕗,𝕒𝕓𝕔𝕖𝕗,𝕕𝕖𝕗,𝕒𝕕𝕖𝕗,𝕓𝕕𝕖𝕗,𝕒𝕓𝕕𝕖𝕗,𝕔𝕕𝕖𝕗,𝕒𝕔𝕕𝕖𝕗,𝕓𝕔𝕕𝕖𝕗,𝕒𝕓𝕔𝕕𝕖𝕗,𝕘,𝕒𝕘,𝕓𝕘,𝕒𝕓𝕘,𝕔𝕘,𝕒𝕔𝕘,𝕓𝕔𝕘,𝕒𝕓𝕔𝕘,𝕕𝕘,𝕒𝕕𝕘,𝕓𝕕𝕘,𝕒𝕓𝕕𝕘,𝕔𝕕𝕘,𝕒𝕔𝕕𝕘,𝕓𝕔𝕕𝕘,𝕒𝕓𝕔𝕕𝕘,𝕖𝕘,𝕒𝕖𝕘,𝕓𝕖𝕘,𝕒𝕓𝕖𝕘,𝕔𝕖𝕘,𝕒𝕔𝕖𝕘,𝕓𝕔𝕖𝕘,𝕒𝕓𝕔𝕖𝕘,𝕕𝕖𝕘,𝕒𝕕𝕖𝕘,𝕓𝕕𝕖𝕘,𝕒𝕓𝕕𝕖𝕘,𝕔𝕕𝕖𝕘,𝕒𝕔𝕕𝕖𝕘,𝕓𝕔𝕕𝕖𝕘,𝕒𝕓𝕔𝕕𝕖𝕘,𝕗𝕘,𝕒𝕗𝕘,𝕓𝕗𝕘,𝕒𝕓𝕗𝕘,𝕔𝕗𝕘,𝕒𝕔𝕗𝕘,𝕓𝕔𝕗𝕘,𝕒𝕓𝕔𝕗𝕘,𝕕𝕗𝕘,𝕒𝕕𝕗𝕘,𝕓𝕕𝕗𝕘,𝕒𝕓𝕕𝕗𝕘,𝕔𝕕𝕗𝕘,𝕒𝕔𝕕𝕗𝕘,𝕓𝕔𝕕𝕗𝕘,𝕒𝕓𝕔𝕕𝕗𝕘,𝕖𝕗𝕘,𝕒𝕖𝕗𝕘,𝕓𝕖𝕗𝕘,𝕒𝕓𝕖𝕗𝕘,𝕔𝕖𝕗𝕘,𝕒𝕔𝕖𝕗𝕘,𝕓𝕔𝕖𝕗𝕘,𝕒𝕓𝕔𝕖𝕗𝕘,𝕕𝕖𝕗𝕘,𝕒𝕕𝕖𝕗𝕘,𝕓𝕕𝕖𝕗𝕘,𝕒𝕓𝕕𝕖𝕗𝕘,𝕔𝕕𝕖𝕗𝕘,𝕒𝕔𝕕𝕖𝕗𝕘,𝕓𝕔𝕕𝕖𝕗𝕘,𝕒𝕓𝕔𝕕𝕖𝕗𝕘};(* scalar, monovector, bivector, trivector, multivector etc. Clifford algebra(etc) elements *)el3={ø,𝕒,𝕒2,𝕓,𝕒𝕓,𝕒2𝕓,𝕔,𝕒𝕔,𝕒2𝕔,𝕓𝕔,𝕒𝕓𝕔,𝕒2𝕓𝕔,𝕕,𝕒𝕕,𝕒2𝕕,𝕓𝕕,𝕒𝕓𝕕,𝕒2𝕓𝕕,𝕔𝕕,𝕒𝕔𝕕,𝕒2𝕔𝕕,𝕓𝕔𝕕,𝕒𝕓𝕔𝕕,𝕒2𝕓𝕔𝕕,𝕖,𝕒𝕖,𝕒2𝕖,𝕓𝕖,𝕒𝕓𝕖,𝕒2𝕓𝕖,𝕔𝕖,𝕒𝕔𝕖,𝕒2𝕔𝕖,𝕓𝕔𝕖,𝕒𝕓𝕔𝕖,𝕒2𝕓𝕔𝕖,𝕕𝕖,𝕒𝕕𝕖,𝕒2𝕕𝕖,𝕓𝕕𝕖,𝕒𝕓𝕕𝕖,𝕒2𝕓𝕕𝕖,𝕔𝕕𝕖,𝕒𝕔𝕕𝕖,𝕒2𝕔𝕕𝕖,𝕓𝕔𝕕𝕖,𝕒𝕓𝕔𝕕𝕖,𝕒2𝕓𝕔𝕕𝕖,𝕗,𝕒𝕗,𝕒2𝕗,𝕓𝕗,𝕒𝕓𝕗,𝕒2𝕓𝕗,𝕔𝕗,𝕒𝕔𝕗,𝕒2𝕔𝕗,𝕓𝕔𝕗,𝕒𝕓𝕔𝕗,𝕒2𝕓𝕔𝕗,𝕕𝕗,𝕒𝕕𝕗,𝕒2𝕕𝕗,𝕓𝕕𝕗,𝕒𝕓𝕕𝕗,𝕒2𝕓𝕕𝕗,𝕔𝕕𝕗,𝕒𝕔𝕕𝕗,𝕒2𝕔𝕕𝕗,𝕓𝕔𝕕𝕗,𝕒𝕓𝕔𝕕𝕗,𝕒2𝕓𝕔𝕕𝕗,𝕖𝕗,𝕒𝕖𝕗,𝕒2𝕖𝕗,𝕓𝕖𝕗,𝕒𝕓𝕖𝕗,𝕒2𝕓𝕖𝕗,𝕔𝕖𝕗,𝕒𝕔𝕖𝕗,𝕒2𝕔𝕖𝕗,𝕓𝕔𝕖𝕗,𝕒𝕓𝕔𝕖𝕗,𝕒2𝕓𝕔𝕖𝕗,𝕕𝕖𝕗,𝕒𝕕𝕖𝕗,𝕒2𝕕𝕖𝕗,𝕓𝕕𝕖𝕗,𝕒𝕓𝕕𝕖𝕗,𝕒2𝕓𝕕𝕖𝕗,𝕔𝕕𝕖𝕗,𝕒𝕔𝕕𝕖𝕗,𝕒2𝕔𝕕𝕖𝕗,𝕓𝕔𝕕𝕖𝕗,𝕒𝕓𝕔𝕕𝕖𝕗,𝕒2𝕓𝕔𝕕𝕖𝕗};(*Element names for tables with ternary symmetry*)

e33={ø,𝕒,𝕒2,𝕓,𝕓2,𝕒𝕓,𝕒2𝕓,𝕒𝕓2,𝕒2𝕓2,
𝕔,𝕒𝕔,𝕒2𝕔,𝕓𝕔,𝕓2𝕔,𝕒𝕓𝕔,𝕒2𝕓𝕔,𝕒𝕓2𝕔,𝕒2𝕓2𝕔,
𝕕,𝕒𝕕,𝕒2𝕕,𝕓𝕕,𝕓2𝕕,𝕒𝕓𝕕,𝕒2𝕓𝕕,𝕒𝕓2𝕕,𝕒2𝕓2𝕕,
𝕔𝕕,𝕒𝕔𝕕,𝕒2𝕔𝕕,𝕓𝕔𝕕,𝕓2𝕔𝕕,𝕒𝕓𝕔𝕕,𝕒2𝕓𝕔𝕕,𝕒𝕓2𝕔𝕕,𝕒2𝕓2𝕔𝕕,
𝕖,𝕒𝕖,𝕒2𝕖,𝕓𝕖,𝕓2𝕖,𝕒𝕓𝕖,𝕒2𝕓𝕖,𝕒𝕓2𝕖,𝕒2𝕓2𝕖,
𝕔𝕖,𝕒𝕔𝕖,𝕒2𝕔𝕖,𝕓𝕔𝕖,𝕓2𝕔𝕖,𝕒𝕓𝕔𝕖,𝕒2𝕓𝕔𝕖,𝕒𝕓2𝕔𝕖,𝕒2𝕓2𝕔𝕖,
𝕕𝕖,𝕒𝕕𝕖,𝕒2𝕕𝕖,𝕓𝕕𝕖,𝕓2𝕕𝕖,𝕒𝕓𝕕𝕖,𝕒2𝕓𝕕𝕖,𝕒𝕓2𝕕𝕖,𝕒2𝕓2𝕕𝕖,𝕔𝕕𝕖,𝕒𝕔𝕕𝕖,𝕒2𝕔𝕕𝕖,𝕓𝕔𝕕𝕖,𝕓2𝕔𝕕𝕖,𝕒𝕓𝕔𝕕𝕖,𝕒2𝕓𝕔𝕕𝕖,𝕒𝕓2𝕔𝕕𝕖,𝕒2𝕓2𝕔𝕕𝕖};(*Element names for tables with double ternary symmetry*)

pick[g_,m_,n_]:=Transpose[Take[Transpose[Take[g,m]],n]];unsign[g_?MatrixQ]:=Module[{l=Length[g],r,e,i,ar,ai,m,p},m=Switch[Length[Union[Flatten[Sign[g]]]],1,p=0;l,2,p=l;2l,_,p=2l;4l];Table[e=g[[j,k]];r=Re[e];ar=Abs[r];i=Im[e];ai=Abs[i];r=ar+If[r<0,p,0];i=ai+Which[i==0,0,i<0,3l,i>0,l];Mod[r+i-1,m]+1,{j,l},{k,l}]];

9.3 Roots of Unity, Generalized signs.

𝕣=.;rus[r_,s_]:=If[r>2,Plus@@Table[-s^i,{i,r-2}]-1,0];signList={𝕙,𝕁,𝕜,𝕞,𝕟,𝕠,𝕡,𝕧,𝕏,𝕐,s,𝕤};rU:={{(𝕙^6)->1,(𝕙^(any_))->(𝕙^(Mod[any,6])),(𝕙^5)->rus[6,𝕙]},{(𝕁^3)->1,(𝕁^(any_))->(𝕁^(Mod[any,3])),(𝕁^2)->-1-𝕁},{(𝕜^(any_?OddQ))->𝕜,(𝕜^(any_?EvenQ))->1,Null},{(𝕞^(any_?OddQ))->𝕞,(𝕞^(any_?EvenQ))->1,Null},{(𝕟^9)->1,(𝕟^(any_))->(𝕟^(Mod[any,9])),(𝕟^8)->rus[9,𝕟]},{(𝕠^8)->1,(𝕠^(any_))->(𝕠^(Mod[any,8])),(𝕠^7)->rus[8,𝕠]},{(𝕡^5)->1,(𝕡^(any_))->(𝕡^(Mod[any,5])),(𝕡^4)->rus[5,𝕡]},{(𝕧^7)->1,(𝕧^(any_))->(𝕧^(Mod[any,7])),(𝕧^6)->rus[7,𝕧]},{(𝕏^4)->1,(𝕏^(any_))->(𝕏^(Mod[any,4])),(𝕏^3)->-1-𝕏-(𝕏^2)},{(𝕐^3)->1,(𝕐^(any_))->(𝕐^(Mod[any,3])),(𝕐^2)->-1-𝕐},{(𝕤^𝕣)->1,(𝕤^(any_))->(𝕤^(Mod[any,𝕣])),(𝕤^(𝕣-1))->rus[Min[3,𝕣],𝕤]}};

Unprotect[Abs,Sign];Abs[𝕙]=1;Abs[𝕁]=1;Abs[𝕜]=1;Abs[𝕞]=1;Abs[𝕟]=1;Abs[𝕠]=1;Abs[𝕡]=1;Abs[𝕤]=1;Abs[𝕧]=1;Abs[𝕏]=1;Abs[𝕐]=1;Sign[𝕙]=𝕙;Sign[𝕁]=𝕁;Sign[𝕜]=𝕜;Sign[𝕞]=𝕞;Sign[𝕟]=𝕟;Sign[𝕠]=𝕠;Sign[𝕡]=𝕡;Sign[𝕤]=𝕤;Sign[𝕧]=𝕧;Sign[𝕏]=𝕏;Sign[𝕐]=𝕐;Protect[Abs,Sign];

findROU[M_,o_:0]:=Module[{v=Variables[M]},rofu={};Do[If[MemberQ[v,signList[[i]]],AppendTo[rofu,If[o==0,rU[[i]],Most[rU[[i]]]]]],{i,Length[signList]}];
rofu=Union[Flatten[rofu]]]

9.4 Predefined Index & Signed Tables.

hoopList names all the loops for which determinant factors have been found, in their order in sections 8.2 et seq (but non-conservative loops are moved to the end).

hoopList={"C2","C4c","C3","C3C2c","C12c","C4C3c","C4","C2C2","Qr","P4","Dav","O2","C8r","CL2","P16c","C8c","C5","C3C2","S3","Q12c","Q12r","D6r","Cl3r","Clm3r","C8","C2C2C2","C4C2","D8","Q8","Octr","Octi","C2C2:C4c","O4","O4a","O4b","C4C4c","C4C4r","Q8C2r","C2D8r","P8","CL3","C4:C4c","QC2r","C2C2:C4r","CL21","CL03","C3C3","C9","C6C3c","C12","C3C2C2","Q12","C2D6","A4","D12","C6C2","C3P4","C6Kr","C3C2C2C2r","D16","Q16","C2D8","C4C4","C2Q8","C2C2C2C2","C4C2C2","C2C2:C4","C4:C4","P16","Oct","Q8M","CL4","CL13","CL22","CL31","CL04","O8","C3C4C2","CL31C2","CL4C2","S3Mn"};

C2=ca[2];C3=ca[3];C3n={{1,2,3},{2,3,1},{3,-1,2}};
C12c={{1,2,3},{2,3,-I},{3,-I,-2 I}};
C4=ca[4];C2C2=ca[4,3];P4={{1,2,3,4},{2,1,-4 I,3 I},{3,4 I,1,-2 I},{4,-3 I,2 I,1}};
C4C3c={{1,2,3},{2,3 I,-1},{3,-1,2 I}};
P16c={{1,2,3,4},{2,-1,-4 I,-3 I},{3,4 I,-1,2 I},{4,3 I,-2 I,1}};Q4n={{1,2,3,4},{2,1,4,-3},{3,-4,1,2},{4,3,-2,1}};
C5=ca[5];C5n={{1,2,3,4,5},{2,1,4,5,3},{3,5,1,2,4},{4,3,5,1,2},{5,4,2,3,1}};
C6=co[C3,C2];S3=ca[6,5];
D3C2c=ms[{6,7},u3];C6n={{1,2,3,4,5,6},{2,3,1,6,4,5},{3,1,2,5,6,4},{4,5,6,2,1,3},{5,6,4,1,3,2},{6,4,5,3,2,1}};

C4C2=co[C4,C2];C2C2C2=co[co[C2,C2],C2];D8=ca[8,7];C8=ca[8];Q8=ca[8,3];Oct=cd[{-1,-1,-1,{2}}];
Q8C2r={{1,2,3,4,5,6,7,8},{2,-5,1,8,-3,-4,6,-7},{3,1,-5,-6,-2,7,-8,4},{4,-6,8,-5,7,-3,-1,2},{5,-3,-2,7,1,8,4,6},{6,7,-4,-2,8,-5,3,-1},{7,-8,6,-1,4,2,-5,-3},{8,4,-7,3,6,-1,-2,-5}};
P8={{1,2,3,4,5,6,7,8},{2,1,-4 I,3 I,6,5,-8 I,7 I},{3,4 I,1,-2 I,7,8 I,5,-6 I},{4,-3 I,2 I,1,8,-7 I,6 I,5},{5,6,7,8,1,2,3,4},{6,5,-8 I,7 I,2,1,-4 I,3 I},{7,8 I,5,-6 I,3,4 I,1,-2 I},{8,-7 I,6 I,5,4,-3 I,2 I,1}};
CL12=cLoop[1,2];

C3C3=co[C3,C3];C12=co[C3,C4];C3C2C2=co[C3,co[C2,C2]];Q12=co[C3,C4,2];(*S3C2=co[C3,co[C2,C2],2];*)A4=ge[{3,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓}];

C3P4=(({{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, {2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10}, {3, 1, 2, 6, 4, 5, 9, 7, 8, 12, 10, 11}, {4, 5, 6, 1, 2, 3, 10 I, 11 I, 12 I, -7 I, -8 I, -9 I}, {5, 6, 4, 2, 3, 1, 11 I, 12 I, 10 I, -8 I, -9 I, -7 I}, {6, 4, 5, 3, 1, 2, 12 I, 10 I, 11 I, -9 I, -7 I, -8 I}, {7, 8, 9, -10 I, -11 I, -12 I, 1, 2, 3, 4 I, 5 I, 6 I}, {8, 9, 7, -11 I, -12 I, -10 I, 2, 3, 1, 5 I, 6 I, 4 I}, {9, 7, 8, -12 I, -10 I, -11 I, 3, 1, 2, 6 I, 4 I, 5 I}, {10, 11, 12, 7 I, 8 I, 9 I, -4 I, -5 I, -6 I, 1, 2, 3}, {11, 12, 10, 8 I, 9 I, 7 I, -5 I, -6 I, -4 I, 2, 3, 1}, {12, 10, 11, 9 I, 7 I, 8 I, -6 I, -4 I, -5 I, 3, 1, 2}}));

D16=ca[16,15];P16i=ge[{2,2,2,2},{𝕒2->𝕕,𝕔𝕓->𝕓𝕔𝕕}];P16a=co[Q8,C2,4];P16=co[P4,C4];C8pC2=co[ca[8],C2,4];g2101=ge[{7,3},{𝕓𝕒->𝕒2𝕓}];OctC2=co[Oct,C2];
SL23=mg[{9,14},u4];P27=ge[{3,3,3},{𝕓𝕒->𝕒𝕓𝕔}];g2704=ge[{9,3},{𝕓𝕒->𝕒4𝕓,𝕓𝕒2->𝕒𝕓}];

(*Large alternative tables*)
Alt12nC2=co[Alt12n,C2];OctrC3=co[Oct,C3];Alt12nC3=co[Alt12n,C3];C4iC4M=(({{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32}, {2, 5, 6, 7, 8, 10, 11, 1, 12, 13, 14, 15, 3, 4, 16, 9, 18, 21, 28, 23, 24, 31, 27, 17, 22, 32, 30, 26, 25, 20, 29, 19}, {3, 12, 4, 9, 10, 2, 6, 16, 1, 11, 15, 7, 8, 13, 5, 14, 25, 28, 17, 19, 31, 18, 22, 32, 20, 21, 26, 23, 24, 29, 27, 30}, {4, 7, 9, 1, 11, 12, 2, 14, 3, 15, 5, 6, 16, 8, 10, 13, 20, 23, 25, 17, 27, 28, 18, 30, 19, 31, 21, 22, 32, 24, 26, 29}, {5, 8, 10, 11, 1, 13, 14, 2, 15, 3, 4, 16, 6, 7, 9, 12, 21, 24, 26, 27, 17, 29, 30, 18, 31, 19, 20, 32, 22, 23, 25, 28}, {6, 15, 7, 12, 13, 5, 10, 9, 2, 14, 16, 11, 1, 3, 8, 4, 28, 31, 23, 22, 32, 27, 26, 25, 18, 30, 29, 21, 20, 19, 24, 17}, {7, 11, 12, 2, 14, 15, 5, 4, 6, 16, 8, 10, 9, 1, 13, 3, 23, 27, 22, 18, 30, 26, 21, 20, 28, 29, 24, 31, 19, 17, 32, 25}, {8, 1, 13, 14, 2, 3, 4, 5, 16, 6, 7, 9, 10, 11, 12, 15, 24, 17, 32, 30, 18, 25, 20, 21, 29, 28, 23, 19, 31, 27, 22, 26}, {9, 6, 1, 3, 15, 7, 12, 13, 4, 5, 10, 2, 14, 16, 11, 8, 19, 22, 20, 25, 26, 23, 28, 29, 17, 27, 31, 18, 30, 32, 21, 24}, {10, 16, 11, 15, 3, 8, 13, 12, 5, 4, 9, 14, 2, 6, 1, 7, 31, 32, 21, 26, 25, 24, 29, 28, 27, 17, 19, 30, 18, 22, 20, 23}, {11, 14, 15, 5, 4, 16, 8, 7, 10, 9, 1, 13, 12, 2, 3, 6, 27, 30, 31, 21, 20, 32, 24, 23, 26, 25, 17, 29, 28, 18, 19, 22}, {12, 10, 2, 6, 16, 11, 15, 3, 7, 8, 13, 5, 4, 9, 14, 1, 22, 26, 18, 28, 29, 21, 31, 19, 23, 24, 32, 27, 17, 25, 30, 20}, {13, 9, 14, 16, 6, 1, 3, 15, 8, 7, 12, 4, 5, 10, 2, 11, 32, 25, 30, 29, 28, 20, 19, 31, 24, 23, 22, 17, 27, 26, 18, 21}, {14, 4, 16, 8, 7, 9, 1, 11, 13, 12, 2, 3, 15, 5, 6, 10, 30, 20, 29, 24, 23, 19, 17, 27, 32, 22, 18, 25, 26, 21, 28, 31}, {15, 13, 5, 10, 9, 14, 16, 6, 11, 1, 3, 8, 7, 12, 4, 2, 26, 29, 27, 31, 19, 30, 32, 22, 21, 20, 25, 24, 23, 28, 17, 18}, {16, 3, 8, 13, 12, 4, 9, 10, 14, 2, 6, 1, 11, 15, 7, 5, 29, 19, 24, 32, 22, 17, 25, 26, 30, 18, 28, 20, 21, 31, 23, 27}, {17, 23, 19, 20, 21, 22, 18, 30, 25, 26, 27, 28, 29, 24, 31, 32, 5, 14, 10, 11, 1, 13, 8, 7, 15, 3, 4, 16, 6, 2, 9, 12}, {18, 27, 22, 23, 24, 26, 21, 20, 28, 29, 30, 31, 19, 17, 32, 25, 8, 4, 16, 14, 2, 9, 1, 11, 13, 12, 7, 3, 15, 5, 6, 10}, {19, 22, 20, 25, 26, 18, 28, 29, 17, 27, 31, 23, 24, 32, 21, 30, 15, 13, 5, 10, 9, 8, 16, 6, 11, 1, 3, 14, 2, 12, 4, 7}, {20, 18, 25, 17, 27, 28, 23, 24, 19, 31, 21, 22, 32, 30, 26, 29, 11, 8, 15, 5, 4, 16, 14, 2, 10, 9, 1, 13, 12, 7, 3, 6}, {21, 30, 26, 27, 17, 29, 24, 23, 31, 19, 20, 32, 22, 18, 25, 28, 1, 7, 3, 4, 5, 6, 2, 14, 9, 10, 11, 12, 13, 8, 15, 16}, {22, 26, 23, 28, 29, 21, 31, 19, 18, 30, 32, 27, 17, 25, 24, 20, 16, 3, 14, 13, 12, 4, 9, 10, 8, 7, 6, 1, 11, 15, 2, 5}, {23, 21, 28, 18, 30, 31, 27, 17, 22, 32, 24, 26, 25, 20, 29, 19, 14, 1, 13, 8, 7, 3, 4, 5, 16, 6, 2, 9, 10, 11, 12, 15}, {24, 20, 29, 30, 18, 19, 17, 27, 32, 22, 23, 25, 26, 21, 28, 31, 2, 11, 12, 7, 8, 15, 5, 4, 6, 16, 14, 10, 9, 1, 13, 3}, {25, 28, 17, 19, 31, 23, 22, 32, 20, 21, 26, 18, 30, 29, 27, 24, 10, 16, 11, 15, 3, 14, 13, 12, 5, 4, 9, 8, 7, 6, 1, 2}, {26, 29, 27, 31, 19, 24, 32, 22, 21, 20, 25, 30, 18, 28, 17, 23, 9, 6, 1, 3, 15, 2, 12, 13, 4, 5, 10, 7, 8, 16, 11, 14}, {27, 24, 31, 21, 20, 32, 30, 18, 26, 25, 17, 29, 28, 23, 19, 22, 4, 2, 9, 1, 11, 12, 7, 8, 3, 15, 5, 6, 16, 14, 10, 13}, {28, 31, 18, 22, 32, 27, 26, 25, 23, 24, 29, 21, 20, 19, 30, 17, 13, 9, 8, 16, 6, 1, 3, 15, 14, 2, 12, 4, 5, 10, 7, 11}, {29, 19, 30, 32, 22, 17, 25, 26, 24, 23, 28, 20, 21, 31, 18, 27, 12, 10, 7, 6, 16, 11, 15, 3, 2, 14, 13, 5, 4, 9, 8, 1}, {30, 17, 32, 24, 23, 25, 20, 21, 29, 28, 18, 19, 31, 27, 22, 26, 7, 5, 6, 2, 14, 10, 11, 1, 12, 13, 8, 15, 3, 4, 16, 9}, {31, 32, 21, 26, 25, 30, 29, 28, 27, 17, 19, 24, 23, 22, 20, 18, 3, 12, 4, 9, 10, 7, 6, 16, 1, 11, 15, 2, 14, 13, 5, 8}, {32, 25, 24, 29, 28, 20, 19, 31, 30, 18, 22, 17, 27, 26, 23, 21, 6, 15, 2, 12, 13, 5, 10, 9, 7, 8, 16, 11, 1, 3, 14, 4}}));

9.5 Main Loop Data File, loop[[mm,nn]]

Unprotect[loop];Clear[loop];

loop=Table[{},{i,169}];

loop[[1]]={{"C1",{1.},0,"ca[1]",{1},{},{},{},{}}};
loop[[2]]={{"C2",{2.},0,"ca[2]",{2},{},{1},{1},{1},{{2,1}}},
{"C4c",{-1.,1,1},0,"cd[{-1}]",{},{},{12},{44},{30}}};
loop[[3]]={{"C3",{1.,(Subscript[1, 2])},0,"ca[3]",{3},{},{10},{8},{8},{{1,2,3}}},{"C3C2c",{-1.,(Subscript[1, 2]),3},0,"cd[{3.}]",{},{},{𝕐},{-8},{-8}},{"C4C3c",{-1. I,(Subscript[1, 2]),4},0,"C4C3c",{},{},{},{},{}},{"C12c",{-1.I,(Subscript[1, 2]),3},22,"C12c",{},{},{},{},{}}};

loop[[4]]={{"C4",{2.,2},0,"ca[4]",{4},{},{12},{13},{12},{{1,2,3,4}}},
{"C2C2",{4.},0,"co[C2,C2]",{2,2},{},{1,2},{1,2},{1,2},{{2,1,4,3},{1,2,4,3}}},
{"Qr",{-3,1,6},0,"cd[{-1,-1}]",{{-2,-2},{2}},{},{13,14},{},{30,31},"0,2"},
{"C2C2r",{-4.,6},0,"cd[{4.}]",{},{},{},{},{}},
{"O2",{-2.,2,4},7,"cd[{-1,1}]",{},{},{3,12},{3,43},{3,30}},{"Dav",{-2.,2,6},2,"cd[{-1,-1.}]",{},{},{12,13},{},{30,41}},
{"CL2",{-1,3,4},0,"cLoop[2]",{{2,2},{2}},{},{2,4},{},{4,5}},
{"P4",{-4I,6},0,"P4",{},{},{},{},{},"msi[{2,3,4}]"},
{"C8r",{-1.,(Subscript[1, 3]),4},0,"ts[ca[8,5]]",{},{},{},{},{}},
{"P16c",{-2I,2,8},0,"P16c",{},{},{},{},{},"msi[{13,2,14}]"}};

loop[[5]]={{"C5",{1.,(Subscript[1, 4])},0,"ca[5]",{5},{},{18},{16},{17},{Range[5]}},{"C10c",{-1.,(Subscript[1, 4]),10},0,"ts[ca[10]]",{},{},{},{-16},{25}},{"C10r",{-1.,(Subscript[1, 4]),9},0,"ts[ca[10],2,{1,3,5,7,4,6,8,10,2,9}]",{},{},{},{},{}},
{"C10s",{-1.,(Subscript[1, 4]),7},0,"ts[ca[10],2,{1,7,8,4,10,6,2,3,9,5}]",{},{},{},{},{}},
{"C10t",{-1.,(Subscript[1, 4]),12},0,"ts[ca[10],2,{1,2,8,4,10,6,7,3,9,5}]",{},{},{},{},{}},
{"C5n",{5},0,"C5n",{},{},{},{},{},{}}};

loop[[6]]={{"S3",{4,(Subscript[1, 2])},0,"ca[6,5]",{3,2},{𝕓𝕒->𝕒2𝕓},{3,10},{2,5},{3,9},{{3,1,2},{2,1,3}}},
{"C6",{2.,(Subscript[2, 2])},72,"co[C3,C2]",{3,2},{},{19 },{17},{18},{Range[6]}},
{"Q12c",{-3,(Subscript[1, 3]),9},0,"ts[Q12]",{},{},{10,13},{},{8,43}},{"Q12r",{-1,(Subscript[1, 2]),3,15},0,"ts[ca[12,5]]",{},{},{},{},{}},
{"D6r",{-1,1,4,12},0,"ts[ca[12,11]]",{},{},{},{},{4,-8}},
{"C3C4c",{-1.`,(Subscript[1, 5]),9},0,"cd[{3,-1.}]",{},{},{10,12},{8,43},{}},
{"Clm3r",{-1.,(Subscript[1, 5]),13},0,"cd[{-3,-1.}]",{},{},{},{},{}},
{"Cl3r",{-1.,(Subscript[1, 5]),15},0,"cd[{3.,-1.}]",{},{},{𝕐 12},{17,44},{26}},
{"C6n",{2,(Subscript[2, 2])},0,"C6n",{},{},{},{},{}}};

loop[[7]]={{"C7",{1.,(Subscript[1, 6])},0,"ca[7]",{7},{},{21},{24},{20},{Range[7]}},{"C14c",{-1.,(Subscript[1, 6]),21},0,"ts[ca[14]]",{},{},{},{-24},{}}};

loop[[8]]={{"C8",{2.,(Subscript[2, 3])},0,"ca[8]",{8},{},{22},{25},{21},{Range[8]}},
{"C4C2",{4.,4},0,"co[C4,C2]",{4,2},{},{1,16},{1,13},{1,16},{{4,1,2,3,8,5,6,7},{5,6,7,8,1,2,3,4}}}, {"D8",{6,2},0,"ca[8,7]",{4,2},{𝕓𝕒->𝕒3𝕓},{2,3},{2,15},{1,3},{{2,1,4,3},{1,3,2,4}}},
{"Q8",{2,6},0,"ca[8,3]",{2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{13,14},{13,14},{15,16},{{2,5,8,3,6,1,4,7},{3,4,5,6,7,8,1,2}}},
{"C2C2C2",{8.},0,"co[C2,C2,C2,1]",{2,2,2},{},{1,2,6},{1,2,3},{1,2,4},{{2,1,4,3,6,5,8,7},{3,4,1,2,7,8,5,6},{7,8,5,6,3,4,1,2}}},{"C16c",{-1.,(Subscript[1, 7]),28},0,"ts[ca[16]]",{},{},{},{},{}},
{"C16r",{-1.,(Subscript[1, 7]),24},0,"ts[ca[16,9]]",{},{},{},{},{}},
{"C4C4c",{-2.,(Subscript[2, 3]),16},0,"cd[{2,1.,-1.}]",{},{},{12,16},{42,44},{}},
{"C4iC4c",{-4,(Subscript[2, 2]),16},0,"ts[co[C4,C4,2]]",{},{},{16,24},{},{}},
{"QC2r",{-6,2,24},20,"ts[co[C2,Q8]]",{2,2,2,{2}},{𝕒2->𝕕,𝕓2->𝕕,𝕓𝕒->𝕒𝕓𝕕},{6,13,14},{},{7,30,44}},
{"Q8C2r",{-6,2,26},0,"Q8C2r",{},{},{},{},{29,30,31}},
{"O4",{-4.,4,16},97,"cd[{1,1,-1.}]",{},{},{4,6,13},{},{}},
{"O4a",{-4.,4,24},0,"cd[{-1,1.,-1.}]",{},{},{3,26,27},{},{}},
{"O4b",{-4.,4,28},0,"cd[{-1,-1.,-1.}]",{},{},{12,26,27},{},{}},
{"P8",{-8I,24},0,"P8",{},{},{},{},{}},
{"KKr",{-8.,24},0,"cd[{4.,1}]",{},{},{},{},{}},
{"C2D8r",{-2,6,16},0,"ts[co[C2,D8]]",{},{},{2,6,25},{},{1,4,5}},
{"CL03",{-6,2,28},0,"cLoop[0,3]",{{-2,-2,-2},{2}},{},{},{},{16,30,44}},
{"CL21",{-2,6,24},0,"cLoop[2,1]",{{2,2,-2},{2}},{},{},{},{4,5,7,16}},
{"CL3",{-4,4,24},0,"cLoop[3]",{{2,2,2},{2}},{},{2,3,13,14},{},{4,29,30},"ts[P16i]"},
{"Octr",{-7,1,28},0,"cd[{-1,-1,-1}]",{},{},{},{},{}},
{"Octi",{-3,5,24},0,"cd[{1,-1,-1}]",{},{},{},{},{}},
{"KiC4r",{-2,2,4,24},0,"ts[co[C2C2,C4,2],2,{1,10,13,14,3,12,15,16,9,2,5,6,11,4,7,8}]",{},{},{9,13},{},{3,43}},
{"C8jC2c",{-2,(Subscript[2, 3]),24},0,"ts[mp[{16,6}],{1,14,3,4,9,6,11,12,5,10,7,8,13,2,15,16}]",{},{},{},{},{}},
{"D8c",{-1,(Subscript[1, 2]),5,24},0,"ts[ca[16,15]]",{},{},{},{},{}},
{"Q8iC2r",{-1,1,(Subscript[3, 2]),24},0,"ts[co[Q8,C2,2],{1,4,3,2,9,14,15,16,5,8,7,6,13,10,11,12}]",{},{},{},{},{}},
{"Q16r",{-1,(Subscript[1, 2]),5,28},0,"ts[ca[16,7]]",{},{},{},{},{}},
{"C4C4r",{-2.,(Subscript[2, 3]),24},12,"cd[{-2,1,-1.}]",{},{},{6,29},{},{}}};

loop[[9]]={{"C9",{1.,(Subscript[1, 8])},1,"ca[9]",{9},{},{23},{28},{23},{Range[9]}},
{"C3C3",{1.,(Subscript[1, 8])},1,"co[C3,C3]",{3,3},{},{},{8,12},{8,11},{{3,1,2,6,4,5,9,7,8},{4,5,6,7,8,9,1,2,3}}},
{"C3C6c",{-1.,(Subscript[1, 8]),27},0,"ts[co[C3,ca[6]]]",{},{},{},{10,-12},{}},
{"C18c",{-1.,(Subscript[1, 8]),36},0,"ts[ca[18]]",{},{},{},{},{}}};

loop[[10]]={{"D10",{6,(Subscript[1, 4])},0,"ca[10,9]",{5,2},{"𝕓𝕒"->"𝕒4𝕓"},{3,18},{2,16},{},{{2,1,5,4,3},{3,4,5,1,2}}},{"C10",{2.,(Subscript[2, 4])},0,"ca[10]",{5,2},{},{1,18},{29},{24},{Range[10]}}};
loop[[11]]={{"C11",{1.,(Subscript[1, 10])},0,"ca[11]",{11},{},{},{},{},{Range[11]}}};

loop[[12]]={{"C3iC4",{2,(Subscript[2, 2]),6},0,"co[C3,C4,2]",{3,4},{𝕓𝕒->𝕒2𝕓},{10,13},{8,36},{8,16},{{2,7,12,5,10,3,8,1,6,11,4,9},{3,4,5,6,7,8,9,10,11,12,1,2}}},{"C12",{2.,(Subscript[2, 5])},0,"co[C3,C4]",{3,4},{},{10,12},{8,15},{26},{Range[12]}},
{"A4",{4,(Subscript[1, 8])},0,"ca[]",{3,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓},{},{3,9},{1,10},{{2,3,1,4},{3,4,1,2}}},
{"D12",{8,(Subscript[2, 2])},0,"ca[12,11]",{3,2,2},{"𝕓𝕒"->"𝕒2𝕓"},{3,19},{2,6},{2,3 },{{1,2,3,5,4},{2,1,4,3,5}}},
{"C6C2",{4.,(Subscript[4, 2])},0,"co[C6,C2]",{3,2,2},{},{1,19},{1,19},{1,19},{{6,4,5,3,1,2,12,10,11,9,7,8},{7,8,9,10,11,12,1,2,3,4,5,6},{8,9,7,11,12,10,2,3,1,5,6,4}}},{"S3Mn",{10,(Subscript[1, 2])},0,"md[S3]",{},{},{},{},{},{{1,2,3,5,4},{2,1,4,3,5}}},{"Alt12n",{4,(Subscript[4, 2])},0,"cd[{-1,-1,{3}}]",{},{},{},{},{},"ge[{2,2,3},{𝕓𝕒->𝕒𝕓𝕔}]"},{"CL20C3",{-1,(Subscript[1, 2]),(Subscript[3, 3]),36},0,"cLoop[2,0,-5]",{},{},{},{},{},"fold[mp[24,10]][[1]]"},
{"CL02C3",{-3,(Subscript[1, 3]),(Subscript[3, 2]),54},0,"cLoop[0,2,-5]",{2,2,3,{2}},{𝕒2->𝕕,𝕓2->𝕕,𝕓𝕒->𝕒𝕓𝕕},{},{},{},"fold[mp[{24,11}]][[1]]"},
{"C3P4",{-4I,(Subscript[4, 2]),54},0,"C3P4",{},{},{},{},{}},
{"C3Dav",{-2.,(Subscript[2, 5]),54},0,"cd[{3,-1.,-1.}]",{2,2,3,{2}},{𝕒2->𝕕,𝕓2->𝕕},{},{},{}},
{"C3iC8r",{-3,(Subscript[1, 6]),3,54},0,"ts[mp[{24,1},1]]",{},{},{10,29},{},{},"fold[mp[24,1]][[1]]"},{"C24r",{-1.,(Subscript[1, 11]),66},0,"ts[mp[{24,2},1]]",{},{},{10,29},{},{},"fold[mp[24,2]][[1]]"},{"SL23r",{-1,(Subscript[1, 8]),3,54},0,"fold[mp[24,3]][[1]]",{},{},{},{},{}},
{"Q24r",{{-1,(Subscript[1, 4]),7,66}},0,"ts[mp[{24,4}]]",{},{},{},{},{},"fold[mp[24,4]][[1]]"},
{"C4S3r",{-1,(Subscript[1, 3]),(Subscript[4, 2]),36},0,"ts[mp[{24,5}]]",{},{},{},{},{},"fold[mp[24,5]][[1]]"},
{"D12r",{-1,(Subscript[1, 4]),7,60},0,"ts[ca[24,23]]",{},{},{},{},{}},
{"C2Q12r",{-2,(Subscript[2, 2]),6,60},0,"ts[co[C2,ca[12,5]]]",{},{},{},{},{}},
{"C3iC4iC2r",{-3,(Subscript[2, 2]),5,36},0,"ts[mp[{24,8},1]]",{},{},{4,10,15},{},{},"msi[{11,2,14}]"},
{"C3r8",{-2.,(Subscript[2, 5]),36},0,"cd[{3,-1.,1}]",{},{},{(*12,19*)},{(*I,2𝕐*)},{(*I,𝕐*)},{"fold[mp[{24,9}]][[1]]"}},
{"C6C2C2c",{-4.,(Subscript[4, 2]),48},0,"cd[{3.,1,1}]",{2,2,3,{2}},{𝕔3->𝕕},{},{},{}},
{"C3C2C2C2r",{-4.,(Subscript[4, 2]),30},0,"ts[co[C2,C3C2C2],2,{1,3, 5,20,22,24,7,21,23,2,4, 6,13,15,17,8,10,12,19,9,11,14,16,18}]",{},{},{},{},{}},
{"C6C2C2r",{-4.,(Subscript[4, 2]),32},0,"cd[{-3,1,1}]",{},{},{},{},{}},
{"C2C2S3r",{-1.,(Subscript[1, 11]),54},0,"ts[co[C3,ca[8],1]]",{},{},{},{},{}},
{"C24r",{-2.,(Subscript[2, 5]),52},0,"cd[{-3,-1.,1}]",{},{},{},{},{}},
{"C24ra",{-2.,(Subscript[2, 5]),60},0,"cd[{3.,-1.,1}]",{2,2,3,{2}},{𝕓2->𝕕,𝕔3->𝕕},{2,𝕐 12},{19,44},{(*2,8I*)}},
{"Cm311",{-2.,(Subscript[2, 5]),62},0,"cd[{-3,-1.,-1.}]",{},{},{},{},{}},
{"C24rb",{-2.,(Subscript[2, 5]),66},0,"cd[{3.,-1.,-1.}]",{2,2,3,{2}},{𝕒2->𝕕,𝕓2->𝕕,𝕔3->𝕕},{13,𝕐 12},{},{}},
{"C36j",{-1.` 𝕁,(Subscript[1, 11]),121},0,"fold[ca[36],{3}][[1]]",{},{},{},{},{}}};

loop[[13]]={{"C13",{1.,(Subscript[1, 12])},0,"ca[13]",{13},{},{},{},{},{Range[13]}}};
loop[[14]]={{"D14",{8,(Subscript[1, 6])},0,"ca[14,13]",{7,2},{𝕓𝕒->𝕒6𝕓},{3,21},{2,24},{},{{2,1,7,6,5,4,3},{3,4,5,6,7,1,2}}},{"C14",{2.,(Subscript[2, 6])},0,"ca[14]",{14},{},{1,21},{30},{1,20},{{Range[14]}}}};
loop[[15]]={{"C15",{1.,(Subscript[1, 14])},0,"ca[15]",{15},{},{10,18},{8,16},{28},{Range[15]}}};

loop[[16]]={
{"C16",{2.,(Subscript[2, 7])},0,"ca[16]",{16},{},{},{},{},{Range[16]}},
{"C4C4",{4.,(Subscript[4, 3])},3,"co[C4,C4]",{4,4},{},{12,16},{15,43},{},{{5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4},{6,7,8,5,10,11,12,9,14,15,16,13,2,3,4,1}}},
{"C2C4iC2",{8,(Subscript[4, 2])},0,"co[C2C2,C4,2]",{4,2,2},{𝕓𝕒->𝕒𝕓𝕔},{9,13},{3,13},{1,13},{{5,8,7,6,9,12,11,10,13,16,15,14,1,4,3,2},{6,7,8,5,10,11,12,9,14,15,16,13,2,3,4,1}}},{"C4iC4",{4,4,8},0,"co[C4,C4,2]",{4,4},{𝕓𝕒->𝕒3𝕓},{13,16},{},{},{{2,5,4,7,6,1,8,3,10,12,9,11},{4,3,6,5,8,7,2,1,12,11,10,9}}},{"C8C2",{4.,(Subscript[4, 3])},3,"co[C8,C2]",{8,2},{},{1,22},{1,25},{1,22},{{8,1,2,3,4,5,6,7,16,9,10,11,12,13,14,15},{9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8}}},{"C8jC2",{4,(Subscript[4, 3])},0,"co[ca[8],C2,4]",{8,2},{"𝕓𝕒"->"𝕒5𝕓"},{29,34},{15,26},{1,21},{{{{8,1,2,3,4,5,6,7},{4,1,6,3,8,5,2,7}}}}},{"D16",{10,(Subscript[2, 3])},0,"ca[16,15]",{8,2},{𝕓𝕒->𝕒7𝕓},{3,22},{},{4,22},{{2,1,16,15,14,13,12,11,10,9,8,7,6,5,4,3},{3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2}}},{"QD16",{6,(Subscript[2, 2]),6},0,"co[Q8,C2,2]",{8,2},{𝕓𝕒->𝕒3𝕓},{},{},{14,37},{{7,4,1,6,3,8,5,2,15,12,9,14,11,16,13,10},{8,7,2,1,4,3,6,5,16,15,10,9,12,11,14,13},{9,16,15,14,13,12,11,10,1,8,7,6,5,4,3,2}}},{"Q16",{2,(Subscript[2, 2]),10},0,"ca[16,7]",{2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕓𝕕,𝕕𝕓->𝕓𝕔𝕕},{},{},{},{{2,9,16,7,14,5,12,3,10,1,8,15,6,13,4,11},{3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,2}}},
{"C4C2C2",{8.,8},0,"co[C4,C2C2]",{4,2,2},{},{1,2,16},{1,3,15},{5,6,12},{{4,1,2,3,8,5,6,7,12,9,10,11,16,13,14,15},{5,6,7,8,1,2,3,4,13,14,15,16,9,10,11,12},{11,12,9,10,15,16,13,14,3,4,1,2,7,8,5,6}}},{"C2D8",{12,4},0,"co[D8,C2]",{4,2,2},{𝕓𝕒->𝕒3𝕓},{1,3,9},{1,2,15},{1,2,5},{{2,1,4,3,6,5,8,7,10,9,12,11,14,13,16,15},{7,4,1,6,3,8,5,2,15,12,9,14,11,16,13,10},{15,12,9,14,11,16,13,10,7,4,1,6,3,8,5,2}}},
{"C2Q8",{4,12},0,"co[Q8,C2]",{2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{6,13,14},{1,13,14},{6,14,30 }},
{"Q8jC2",{8,8},0,"co[ca[8,3],C2,4]",{2,2,2,2},{𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{2,3,4 },{ },{1,7,16},{{2,1,8,15,6,5,12,3,10,9,16,7,14,13,4,11},{3,16,1,6,7,4,5,10,11,8,9,14,15,12,13,2},{4,7,14,1,8,11,2,5,12,15,6,9,16,3,10,13},{5,6,7,8,9,10,11,12,13,14,15,16,1,2,3,4}},"co[P4,C4]"},
{"C2C2C2C2",{16.},0,"co[C2,C2,C2,C2,1]",{2,2,2,2},{},{1,2,6,8},{},{}},
{"Oct",{2,14},0,"Oct",{},{},{},{},{}},{"D8Mn",{14,2},0,"md[D8]",{},{},{},{},{},"cd[{1,-1,-1,{2}}]"},
{"Q8M",{10,6},98,"md[Q8]",{},{},{},{},{},"cd[{1,-1,-1,{2}}]"},
{"CL4",{-10,6,112},15,"cLoop[4]",{{2,2,2,2},{2}},{},{},{},{}},
{"CL31",{-6,10,112},13,"cLoop[3,1]",{{2,2,2,-2},{2}},{},{},{},{}},
{"CL22?",{-6,10,112},13,"cLoop[2,2]",{{2,2,-2,-2},{2}}
,{},{},{},{}},
{"CL13?",{-10,6,112},15,"cLoop[1,3]",{{2,-2,-2,-2},{2}},{},{},{},{}},
{"CL04",{-10,6,120},0,"cLoop[0,4]",{{-2,-2,-2,-2},{2}},{},{},{},{},{}},
{"PD16",(*Variation on CL04??*){-10,6,118},0,"ca[]",{},{},{},{},{1,-29,-30,15}},
{"O8",{-8.,8,64},0,"cd[{1,1,1,-1.}]",{},{},{},{},{}},
{"(C2^5)r",{-16.,96},0,"cd[{4.,1,1}]",{},{},{},{},{}},
{"C4C2C2C2r",{-8.,8,112},0,"cd[{4.,1,-1.}]",{},{},{},{},{}},
{"O8a",{-4.,(Subscript[4, 3]),64},0,"cd[{4,1,-1.}]",{},{},{},{},{}}};

loop[[17]]={{"C17",{1.,(Subscript[1, 16])},0,"ca[17]",{17},{},{},{},{},{Range[17]}}};
loop[[18]]={{"D18",{10,(Subscript[1, 8])},6,"ca[18,17]",{9,2},{𝕓𝕒->𝕒8𝕓},{3,23},{2,28},{},{{2,1,9,8,7,6,5,4,3},{3,4,5,6,7,8,9,1,2}}},
{"C18",{2.,(Subscript[2, 8])},5,"ca[18]",{18},{},{1,23},{31},{1,23},{Range[17]}},
{"C3S3",{4,(Subscript[1, 6]),(Subscript[4, 2])},0,"co[C3,S3]",{3,6},{𝕓𝕒->𝕒2𝕓},{4,32},{2,9},{2,11},{{5,6,7,8,1,2,3,4},{4,2,1,3,5,6,7,8}}},
{"C3iS3",{10,(Subscript[1, 8])},6,"co[C3,ca[6,5],2]",{2,3,3},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2},{3,10,11},{2,8,32},{}},
{"Q36r",{-1,(Subscript[1, 8]),9,153},0,"fold[mp[{36,1}]][[1]]",{},{},{},{},{}},
{"D36r",{-1,(Subscript[1, 7]),10,144},0,"fold[mp[{36,4}]][[1]]",{},{},{},{},{}},
{"Q12C3r",{-3,(Subscript[1, 9]),(Subscript[3, 2]),81},0,"fold[mp[{36,6}]][[1]]",{},{},{},{},{}},
{"C3iQ12r",{-1,(Subscript[1, 8]),9,135},0,"fold[mp[{36,7}]][[1]]",{},{},{},{},{}},
{"C12C3r",{-1.`,(Subscript[1, 17]),135},0,"fold[mp[{36,8}]][[1]]",{},{},{},{},{}},
{"C2C3C3iC2r",{-1,(Subscript[1, 7]),10,108},0,"fold[mp[{36,13}]][[1]]",{},{},{},{},{}}};
loop[[19]]={{"C19",{1.,(Subscript[1, 18])},0,"ca[19]",{19},{},{},{},{},{Range[19]}}};

loop[[20]]={{"C5iC4",{6,(Subscript[1, 4]),(Subscript[2, 5])},0,"ca[]",{5,4},{𝕓𝕒->𝕒2𝕓},{},{},{},{{2,5,3,1,4},{3,4,5,1,2}}},{"C20",{2.,(Subscript[2, 9])},0,"ca[20]",{20},{},{12,18},{15,16},{12,17}},
{"Q20",{2,(Subscript[2, 4]),10},0,"ca[20,9]",{5,4},{𝕓𝕒->𝕒4𝕓},{13,18},{},{}},
{"D20",{12,(Subscript[2, 4])},0,"ca[20,19]",{10,2},{𝕓𝕒->𝕒9𝕓},{3,-18},{2,29},{}},{"C10C2",{4.,(Subscript[4, 4])},0,"co[ca[10],C2]",{10,2},{},{2,-18},{3,29},{1,25}}};
loop[[21]]={{"C7iC3",{1,(Subscript[1, 20])},0,"co[ca[7],C3,7]",{7,3},{𝕓𝕒->𝕒2𝕓},{},{},{}},{"C21",{1.,(Subscript[1, 20])},0,"ca[21]",{21},{},{10,21},{8,24},{8,20},{{8,1,9,6,5,3,7,4,2,11,12,10}}}};
loop[[22]]={{"D22",{12,(Subscript[1, 10])},0,"ca[22,21]",{11,2},{𝕓𝕒->𝕒10𝕓},{},{},{}},
{"C22",{2.,(Subscript[2, 10])},0,"co[ca[11],C2]",{22},{},{},{},{}}};
loop[[23]]={{"C23",{1.,(Subscript[1, 22])},0,"ca[23]",{23},{},{},{},{}}};

loop[[24]]={{"C3iC8",{2,(Subscript[2, 5]),(Subscript[6, 2])},0,"co[C3,C8,2]",{3,8},{𝕓𝕒->𝕒2𝕓},{10,35},{8,26},{}},{"C24",{2.,(Subscript[2, 11])},0,"ca[24]",{24},{},{10,22},{8,27},{8,22},{{8,1,9,6,5,3,4,7,2,11,12,10}}},{"SL(2,3)",{2,(Subscript[2, 8]),6},0,"ca[]",{3,2,2,2},{𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔𝕕,𝕕𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕔𝕕},{},{},{9,14},{{{3,7,5},{4,8,6}},{{1,5,2,6},{3,8,4,7}},{{1,3,2,4},{5,7,6,8}},{{1,2},{3,4},{5,6},{7,8}}}},
{"Q24",{2,(Subscript[2, 4]),14},0,"ca[24,11]",{3,2,2,2},{𝕓𝕒->𝕒2𝕓,𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{13,15},{},{14,27}},
{"C4S3",{8,(Subscript[2, 4]),8},0,"co[S3,C4]",{3,2,4},{𝕓𝕒->𝕒2𝕓},{3,15},{2,46},{27,29},{{4,1,2,3,8,5,6,7,12,9,10,11},{5,6,7,8,1,2,3,4,9,10,11,12},{11,12,9,10,3,4,1,2,7,8,5,6}}},{"D24",{14,(Subscript[2, 5])},0,"ca[24,23]",{12,2},{𝕓𝕒->𝕒11𝕓},{3,5},{2,8,15},{34,39,40}},
{"C2Q12",{4,(Subscript[4, 2]),12},0,"co[ca[12,5],C2]",{6,4},{𝕓𝕒->𝕒5𝕓},{13,19},{},{1,8,16}},{"C6C2iC2",{10,(Subscript[4, 2]),6},0,"co[C3,C4,C2,2,2]",{6,2,2},{𝕓𝕒->𝕒5𝕓𝕔},{3,20},{3,5,7},{3,19}},
{"C12C2",{4.,(Subscript[4, 5])},0,"co[C12,C2]",{3,4,2},{},{12,19},{13,17},{5,27}},{"C3D8",{6,(Subscript[2, 3]),(Subscript[6, 2])},0,"co[D8,C3]",{4,2,3},{𝕓𝕒->𝕒3𝕓},{2,32},{5,22},{1,27},{{5,8,7,6,9,12,11,10,1,4,3,2}{6,7,8,5,10,11,12,9,2,3,4,1}}},
{"C3Q8",{2,(Subscript[2, 2]),(Subscript[6, 3])},0,"co[Q8,C3]",{2,2,2,3},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{12,13,14},{}},
{"S4",{10,(Subscript[1, 8]),(Subscript[2, 3])},0,"sgroup[4]",{3,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓,𝕕𝕒->𝕒2𝕕,𝕕𝕓->𝕔𝕕,𝕕𝕔->𝕓𝕕},{},{2,11},{2,9},{{2,3,4,1},{1,2,4,3}}},
{"C2A4",{8,(Subscript[2, 8])},0,"co[Transpose[A4],C2]",{3,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓},{},{3,20},{1,9},{{6,4,5,3,1,2},{6,1,2,3,4,5},{2,3,1,5,6,4}}},{"C2C2S3",{16,(Subscript[4, 2])},0,"co[ca[12,11],C2]",{6,2,2},{𝕓𝕒->𝕒5𝕓},{1,3,19},{2,3,18},{3,-9,18}},
{"C6C2C2",{8.,(Subscript[8, 2])},0,"co[C3,C2,C2,C2,1]",{3,2,2,2},{},{1,2,19},{1,2,22},{1,5,19}},
{"CL21C3",{-2,(Subscript[2, 2]),(Subscript[6, 3]),216},0,"cLoop[2,1,-5]",{},{},{},{},{},{},{}},{"CL12C3",{-4,(Subscript[4, 5]),216},0,"cLoop[1,2,-5]",{},{},{},{},{}},
{"CL03C3",{-6,(Subscript[2, 3]),(Subscript[6, 2]),252},0,"cLoop[0,3,-5]",{},{},{},{},{}},
{"OctrC3",{{-7,(Subscript[1, 3]),(Subscript[7, 2]),252}},0,"cLoop[0,0,-1]",{},{},{},{},{}},{"OctiC3",{{-3,(Subscript[3, 2]),(Subscript[5, 3]),216}},0,"cLoop[0,0,-2]",{},{},{},{},{}}};

loop[[25]]={{"C25",{1.,(Subscript[1, 24])},9,"ca[25]",{25},{},{},{},{}},{"C5C5",{1.,(Subscript[1, 24])},9,"co[ca[5],ca[5]]",{5,5},{},{},{},{}}};
loop[[26]]={{"D26",{14,(Subscript[1, 12])},0,"ca[26,25]",{13,2},{𝕓𝕒->𝕒12𝕓},{},{},{}},
{"C26",{2.,(Subscript[2, 12])},0,"ca[26]",{26},{},{},{},{}}};
loop[[27]]={{"C27",{1.,(Subscript[1, 26])},8,"ca[27]",{27},{},{},{},{}},{"C9C3",{1.,(Subscript[1, 26])},8,"co[ca[9],C3]",{9,3},{},{10,23},{8,28},{8,23}},{"C3C3iC3",{1,(Subscript[1, 26])},10,"ca[]",{3,3,3},{𝕓𝕒->𝕒𝕓𝕔},{},{8,9 },{8,10 }},
{"C9iC3",{1,(Subscript[1, 26])},10,"ca[]",{9,3},{𝕓𝕒->𝕒4𝕓},{},{},{}},
{"C3C3C3",{1.,(Subscript[1, 26])},8,"co[C3C3,C3]",{3,3,3},{},{},{},{}}};
loop[[28]]={{"Q28",{2,(Subscript[2, 6]),14},0,"ca[28,13]",{7,4},{𝕓𝕒->𝕒6𝕓},{13,21},{},{}},
{"C28",{2.,(Subscript[2, 13])},0,"ca[28]",{28},{},{12,21},{15,24},{12,20}},{"D28",{16,(Subscript[2, 6])},0,"ca[28,27]",{14,2},{𝕓𝕒->𝕒13𝕓},{3,-21},{2,30},{}},{"C14C2",{4.,(Subscript[4, 6])},0,"co[ca[14],C2]",{14,2},{},{2,-21},{3,30},{1,-20}},
{"D14Mn",{22,(Subscript[1, 6])},0,"md[ca[14,13]]",{},{},{},{},{}}};

loop[[29]]={{"C29",{1.,(Subscript[1, 28])},0,"ca[29]",{29},{},{},{},{}}};
loop[[30]]={{"C5S3",{4,(Subscript[1, 10]),(Subscript[4, 4])},0,"ca[30,11]",{3,10},{𝕓𝕒->𝕒2𝕓},{},{},{3,28}},{"C3D10",{6,(Subscript[1, 12]),(Subscript[6, 2])},0,"ca[30,19]",{15,2},{𝕓𝕒->𝕒4𝕓},{18,32},{16,19},{}},
{"D30",{16,(Subscript[1, 14])},0,"ca[30,29]",{15,2},{"𝕓𝕒"->"𝕒14𝕓"},{3,10,18},{2,8,16},{}},
{"C30",{2.,(Subscript[2, 14])},0,"ca[30]",{30},{},{18,19},{8,29},{8,25}}};
loop[[31]]={{"C31",{1.,(Subscript[1, 30])},0,"ca[31]",{31},{},{},{},{}}};

loop[[32]]={{"C32",{2.,(Subscript[2, 15]),1},0,"ca[32]",{32},{},{},{},{}},{"C4C2jC4",{8,(Subscript[8, 3]),19},11,"co[co[C4,C2],C4,4]",{4,4,2},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"C8C4",{4.,(Subscript[4, 7]),7},0,"co[C8,C4]",{8,4},{},{12,22},{15,27},{12,22}},{"C8jC4",{4,(Subscript[4, 7]),7},0,"co[C8,C4,4]",{8,4},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"C2C2iC8",{8,(Subscript[4, 4]),8,11},14,"co[C2C2,C8,2]",{8,2,2},{𝕓𝕒->𝕒𝕓𝕔},{2,35},{3,25},{}},{"C4C2iC2iC2",{12,(Subscript[4, 5]),23},0,"ca[]",{4,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕},{},{},{5,13}},{"C8iC2iC2",{12,(Subscript[4, 5]),15},0,"ca[]",{8,2,2},{𝕓𝕒->𝕒5𝕓,𝕔𝕒->𝕒𝕓𝕔},{},{},{7,37}},
{"C2kC4C2iC2",{4,(Subscript[4, 4]),12,7},0,"ca[]",{2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"D8iC4",{12,(Subscript[4, 3]),8,19},0,"co[D8,C4,2]",{8,2,2},{𝕓𝕒->𝕒3𝕓𝕔},{3,17},{},{}},

{"Q8iC4",{4,(Subscript[4, 2]),8,12,11},0,"co[Q8,C4,2]",{2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},
{"C4C4jC2",{8,(Subscript[4, 4]),8,11},14,"ca[]",{2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖},{3,29},{2,26},{3,12},{{5,6,7,8,1,2,3,4},{4,1,2,3,5,6,7,8}}},{"C4iC8",{4,(Subscript[4, 3]),(Subscript[8, 2]),7},0,"co[C4,C8,2]",{4,8},{𝕓𝕒->𝕒3𝕓},{34,35},{},{}},{"Q8jC4",{4,(Subscript[4, 3]),(Subscript[8, 2]),11},0,"co[ca[8,5],C4,2]",{8,4},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"C8iC4",{4,(Subscript[4, 3]),16,11},0,"co[C8,C4,2]",{8,4},{𝕓𝕒->𝕒7𝕓},{13,17},{13,27},{16,22}},{"C4kD8",{4,(Subscript[4, 3]),(Subscript[8, 2]),3},0,"ca[]",{2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕔,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"C16C2",{4.,(Subscript[4, 7]),3},0,"co[ca[16],C2]",{16,2},{},{},{},{}},
{"C16jC2",{4,(Subscript[4, 7]),3},0,"ca[]",{16,2},{𝕓𝕒->𝕒9𝕓},{},{},{}},
{"D32",{18,(Subscript[2, 7]),9},0,"ca[32,31]",{16,2},{𝕓𝕒->𝕒15𝕓},{},{},{}},
{"QD32",{10,(Subscript[2, 6]),10,9},0,"co[ca[16,7],C2,2]",{16,2},{𝕓𝕒->𝕒7𝕓},{},{},{}},

{"Q32",{2,(Subscript[2, 6]),18,9},0,"ca[32,15]",{2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"C4C4C2",{8.,(Subscript[8, 3]),19},0,"co[C4,C4,C2,1]",{4,4,2},{},{2,12,16},{},{}},{"C2C2jC4C2",{16,(Subscript[8, 2]),43},0,"co[C2C2,co[C4,C2],2]",{4,2,2,2},{𝕓𝕒->𝕒𝕓𝕔},{6,9,13},{},{2,4,12}},{"C2C4iC4",{8,8,16,19},17,"co[C4,C4,C2,1,2]",{4,4,2},{𝕓𝕒->𝕒3𝕓},{6,13,16},{},{}},
{"C2C4jC4",{8,(Subscript[8, 3]),19},11,"co[co[C2,C4],C4,4]",{4,2,4},{𝕓𝕒->𝕒𝕓𝕔2},{},{},{}},
{"C4D8",{12,(Subscript[4, 2]),12,23},18,"co[ca[8,7],C4]",{4,2,4},{𝕓𝕒->𝕒3𝕓},{3,9,12},{},{2,5,12}},
{"C4Q8",{4,4,(Subscript[12, 2]),15},19,"co[Q8,C4]",{2,2,2,4},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"C2C2iC2C2iC2"(*P32*),{20,(Subscript[4, 3]),47},0,"co[C2C2,C2C2,C2,2,2]",{4,2,2,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔𝕕},{},{3,5,34},{1,2,7}},
{"C2C2iD8",{16,(Subscript[8, 2]),27},0,"co[C2C2,D8,2]",{4,2,4},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔3},{2,3,9},{},{4,5,12}},
{"C2C2iQ8",{8,8,16,19},17,"co[C2C2,Q8,2]",{2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕𝕖},{},{3,13,14},{2,14,30}},

{"C4C2C2jC2",{12,(Subscript[4, 2]),12,23},18,"ca[]",{2,2,2,2,2},{𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"C4C4jkC2",{12,(Subscript[4, 2]),12,23},18,"ca[]",{2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{9,13,14},{},{}},{"C2C2kC2C2C2",{4,4,(Subscript[12, 2]),15},19,"ca[]",{2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"C4C4jC2",{8,(Subscript[8, 3]),19},11,"ca[]",{2,2,2,2,2},{𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"C4iD8",{20,(Subscript[4, 3]),31},0,"co[C4,D8,2]",{4,4,2},{𝕔𝕓->𝕓3𝕔,𝕔𝕒->𝕒3𝕔},{3,4,9},{},{}},
{"C4iQ8",{4,(Subscript[4, 2]),20,15},0,"co[C4,Q8,2]",{4,2,2,2},{𝕓𝕒->𝕒3𝕓,𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{13,14,16},{},{}},
{"C8C2C2",{8.,(Subscript[8, 3]),11},0,"co[C8,C2C2]",{8,2,2},{},{1,2,22},{1,3,26},{1,2,22}},
{"C2C8jC2",{8,(Subscript[8, 3]),11},0,"co[C2,ca[8],C2,4]",{8,2,2},{𝕓𝕒->𝕒5𝕓},{},{1,15,26},{1,5,21}},{"C8C2jkC2",{8,(Subscript[8, 3]),7},99,"ca[]",{2,2,2,2,2},{𝕒2->𝕕,𝕕2->𝕖,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},{"C2D16",{20,(Subscript[4, 3]),27},0,"co[D8,C2C2,2]",{8,2,2},{𝕓𝕒->𝕒7𝕓},{1,3,22},{},{1,4,22}},

{"C2QD16",{12,(Subscript[4, 2]),12,19},0,"co[Q8,C2C2,2]",{8,2,2},{𝕓𝕒->𝕒3𝕓},{},{},{}},
{"C2D16",{4,(Subscript[4, 2]),20,11},0,"co[ca[16,7],C2]",{2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕓𝕔,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"C8C2iC2",{12,(Subscript[4, 2]),12,11},0,"ca[]",{2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕓𝕔,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},{"C2D8iC2",{16,(Subscript[4, 2]),8,19},0,"ca[]",{8,2,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒5𝕔},{},{},{}},
{"C2Q8jC2",{8,(Subscript[4, 2]),16,11},0,"ca[]",{2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕓𝕔,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕔->𝕔𝕕𝕖},{},{},{}},{"C4C2C2C2",{16.,16,43},0,"co[C4,C2C2,C2,1]",{4,2,2,2},{},{4,6,8,12},{},{}},
{"C2C2D8",{24,8,67},0,"co[D8,C2C2]",{4,2,2,2},{𝕓𝕒->𝕒3𝕓},{1,3,6,9},{1,2,3,15},{}},
{"C2C2Q8",{8,24,19},0,"co[Q8,C2C2]",{2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{6,8,13,14},{1,3,4,15,36},{}},
{"C2C4C2iC2"(*PC2*),{16,16,27},0,"co[co[Q8,C2,4],C2]",{2,2,2,2,2},{𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{2,3,4,6},{},{5,7,29,30}},
{"C2D8jC2",{20,12,39},0,"co[cLoop[3,1],C2]",{2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕖𝕕->𝕔𝕕𝕖},{},{},{1,4,5,7}},
{"C2D8kC2",{12,20,15},0,"co[cLoop[4],C2]",{2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕕𝕔->𝕔𝕕𝕖},{},{},{1,29,30,31}},

{"C2C2C2C2C2",{32.,155},0,"co[C2C2,co[C2C2,C2]]",{2,2,2,2,2},{},{},{},{}},
{"CL50",{-20,12,3},0,"cLoop[5.]",{{2,2,2,2,2},{2}},{},{},{},{}},{"CL41",{-16,16,7},0,"cLoop[4.,1]",{{2,2,2,2,-2},{2}},{},{},{},{}},{"CL32",{-12,20,17},0,"cLoop[3.,2]",{{2,2,2,-2,-2},{2}},{},{},{},{}},{"CL23?",{-16,16,7},0,"cLoop[2.,3]",{{2,2,-2,-2,-2},{2}},{},{},{},{}},
{"CL14?",{-20,12,3},0,"cLoop[1.,4]",{{2,-2,-2,-2,-2},{2}},{},{},{},{}},
{"CL05?",{-16,16,7},0,"cLoop[0.,5]",{{-2,-2,-2,-2,-2},{2}},{},{},{},{}},{"OctC2",{{4,28,15}},0,"co[Oct,C2]",{},{},{},{},{}},{"OctiC2n",{6,(Subscript[2, 2]),(Subscript[4, 2]),14,9},0,"co[Oct,C2,2]",{},{},{},{},{}},{"P16M",{16,16,15},0,"md[co[P4,C4],{1,10,11,12,5,14,15,16,9,2,3,4,13,6,7,8}]",{},{},{},{},{}},{"C8pC2M",{8,(Subscript[8, 3]),7},99,"md[co[ca[8],C2,4],{1,6,3,8,5,2,7,4,13,14,15,16,9,10,11,12}]",{},{},{},{},{}},
{"KiC4M",{12,4,(Subscript[8, 2]),23},0,"md[co[C2C2,C4,2],{1,4,3,2,7,8,5,6,9,12,11,10,15,16,13,14}]",{},{},{},{},{}},
{"Q8C2M",{20,12,31},0,"md[co[Q8,C2]]",{},{},{},{},{}},{"C4iC4M",{4,12,16,15},0,"C4iC4M",{},{},{},{},{}},{"O16",{-16.`,16,35},0,"cd[{-1,1,1,1,1}]",{},{},{},{},{}}};

loop[[33]]={{"C33",{1.,(Subscript[1, 32])},0,"ca[33]",{11,3},{},{},{},{}}};
loop[[34]]={{"C34",{2.,(Subscript[2, 16])},0,"ca[34]",{34},{},{},{},{}},{"D34",{18,(Subscript[1, 16])},0,"ca[34,33]",{17,2},{𝕓𝕒->𝕒16𝕓},{},{},{}}};
loop[[35]]={{"C35",{1.,(Subscript[1, 34])},0,"ca[35]",{7,5},{},{18,21},{16,24},{17,20}}};

loop[[36]]={{"Q36",{2,(Subscript[2, 8]),18},26,"ca[36,17]",{9,4},{𝕓𝕒->𝕒8𝕓},{13,23},{},{}},{"C36",{2.`,(Subscript[2, 17])},23,"ca[36]",{36},{},{12,23},{15,28},{12,23}},{"C2C2iC9",{4,(Subscript[1, 24]),(Subscript[4, 2])},27,"ca[]",{3,3,2,2},{𝕒3->𝕓,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕔},{},{},{}},{"D36",{20,(Subscript[2, 8])},25,"ca[36,35]",{18,2},{𝕓𝕒->𝕒17𝕓},{3,-23},{2,31},{}},{"C18C2",{4.`,(Subscript[4, 8])},24,"co[ca[18],C2]",{18,2},{},{6,7},{3,31},{1,-23}},{"Q12C3",{2,(Subscript[2, 8]),(Subscript[6, 3])},0,"co[Q12,C3]",{12,3},{𝕓𝕒->𝕒𝕓2},{},{8,13},{8,14}},
{"C3iQ12",{2,(Subscript[2, 8]),18},26,"co[C3,ca[12,5],2]",{3,4,3},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓𝕔2},{10,11,13},{},{}},{"C12C3",{2.,(Subscript[2, 17])},23,"co[ca[12],C3]",{12,3},{},{10,11,12},{8,12,15},{8,11,12}},
{"C3C3jC4",{10,(Subscript[1, 8]),(Subscript[2, 9])},0,"ca[]",{4,3,3},{𝕓𝕒->𝕒𝕔,𝕔𝕒->𝕒𝕓2},{},{},{8,13},S3{{2,3,4,1,6,5},{5,6,1,2,3,4}}},

{"S3S3",{16,(Subscript[1, 4]),(Subscript[4, 4])},0,"co[S3,S3]",{3,2,3,2},{𝕓𝕒->𝕒2𝕓,𝕕𝕔->𝕔2𝕕},{},{},{32,33}},
{"C3A4",{4,(Subscript[1, 24]),(Subscript[4, 2])},27,"co[Transpose[A4],C3]",{3,2,2,3},{𝕔𝕒->𝕒𝕓,𝕓𝕒->𝕒𝕓𝕔},{},{9,22},{1,10,11}},
{"C6S3",{8,(Subscript[2, 6]),(Subscript[8, 2])},0,"co[C6,S3]",{6,6},{𝕓𝕒->𝕒5𝕓},{19,32},{2,23},{7,19}},
{"C2C3C3iC2",{20,(Subscript[2, 8])},25,"co[ca[6],ca[6,5],2]",{2,3,3,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2},{3,10,19},{2,18,32},{}},
{"C6C6",{4.,(Subscript[4, 8])},24,"co[ca[6],ca[6]]",{6,6},{},{19,20},{18,22},{-8,19}},{"D18Mn?",{28,(Subscript[1, 8])},0,"md[ca[18,17]]",{},{},{},{},{}},
{"D3C3Mn",{22,(Subscript[1, 6]),(Subscript[4, 2])},0,"md[co[S3,C3]]",{},{},{},{},{}},
{"E18Mn?",{28,(Subscript[1, 8])},0,"md[co[C3,ca[6,5],2]]",{},{},{},{},{}}};

loop[[37]]={{"C37",{1.,(Subscript[1, 36])},0,"ca[37]",{37},{},{},{},{}}};
loop[[38]]={{"C38",{2.,(Subscript[2, 18])},0,"ca[38]",{38},{},{},{},{}},{"D38",{20,(Subscript[1, 18])},0,"ca[38,37]",{19,2},{𝕓𝕒->𝕒18𝕓},{},{},{}}};
loop[[39]]={{"C13iC3",{1,(Subscript[1, 38])},0,"ca[]",{13,3},{𝕓𝕒->𝕒3𝕓},{},{},{}},
{"C39",{1.,(Subscript[1, 38])},0,"ca[39]",{13,3},{},{},{},{}}};

loop[[40]]={{"C5iC8",{2,(Subscript[2, 9]),(Subscript[10, 2])},0,"ca[40,9]",{5,8},{𝕓𝕒->𝕒4𝕓},{18,35},{16,26},{}},
{"C40",{2.`,(Subscript[2, 19])},0,"ca[40]",{40},{},{18,22},{16,27},{17,22}},{"C5jC8",{2,(Subscript[2, 14]),10},0,"ca[]",{5,8},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"Q40",{2,(Subscript[2, 8]),22},0,"ca[40,19]",{5,2,2,2},{𝕓𝕒->𝕒4𝕓,𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{13,14,18},{},{}},
{"C4D10",{12,(Subscript[2, 8]),12},0,"co[ca[10,9],C4]",{20,2},{𝕓𝕒->𝕒9𝕓},{3,12,18},{},{}},
{"D40",{22,(Subscript[2, 9])},0,"ca[40,39]",{20,2},{𝕓𝕒->𝕒19𝕓},{3,4,18},{2,15,16},{}},
{"C10iC4",{4,(Subscript[4, 4]),20},0,"co[ca[10],C4,2]",{5,4,2},{𝕓𝕒->𝕒4𝕓},{6,13,18},{},{}},
{"C2C2iD10",{14,(Subscript[4, 4]),10},0,"co[C2C2,ca[10,9],2]",{5,4,2},{𝕓𝕒->𝕒4𝕓,𝕔𝕓->𝕓3𝕔},{2,3,18},{},{}},{"C20C2",{4.`,(Subscript[4, 9])},0,"co[ca[20],C2]",{20,2},{},{16,-18},{15,29},{12,25}},

{"C5D8",{6,(Subscript[2, 5]),(Subscript[6, 4])},0,"ca[40,31]",{4,10},{𝕓𝕒->𝕒3𝕓},{},{37,40},{1,24}},{"C5Q8",{2,(Subscript[2, 4]),(Subscript[6, 5])},0,"ca[40,11]",{5,2,2,2},{𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},{"C2C5jC4",{12,(Subscript[2, 4]),(Subscript[4, 5])},0,"ca[]",{5,4,2},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C2C2D10",{24,(Subscript[4, 4])},0,"co[ca[10,9],C2C2]",{5,2,2,2},{𝕓𝕒->𝕒4𝕓},{3,6,-18},{2,3,29},{}},{"C10C2C2",{8.`,(Subscript[8, 4])},0,"co[ca[10],C2C2]",{10,2,2},{},{2,6,-18},{},{1,5,25}}};

loop[[41]]={{"C41",{1.,(Subscript[1, 40])},0,"ca[41]",{41},{},{},{},{}}};
loop[[42]]={{"C7iC3iC2",{8,(Subscript[1, 6]),(Subscript[2, 14])},0,"ca[]",{7,6},{𝕓𝕒->𝕒3𝕓},{},{},{},{{2,7,5,3,1,6,4},{2,3,4,5,6,7,1}}},
{"C2C7iC3",{2,(Subscript[2, 20])},0,"ca[]",{7,6},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C7S3",{4,(Subscript[1, 14]),(Subscript[4, 6])},0,"ca[42,29]",{3,7,2},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C3D14",{8,(Subscript[1, 18]),(Subscript[8, 2])},0,"ca[42,13]",{21,2},{𝕓𝕒->𝕒13𝕓},{21,32},{19,24},{}},
{"D42",{22,(Subscript[1, 20])},0,"ca[42,41]",{21,2},{𝕓𝕒->𝕒20𝕓},{3,10,21},{2,8,24},{}},
{"C42",{2.`,(Subscript[2, 20])},0,"ca[42]",{42},{},{19,21},{8,30},{19,20},{{8,9,1,5,6,3,4,7,2,11,12,10}}}
};
loop[[43]]={{"C43",{1.,(Subscript[1, 42])},0,"ca[43]",{43},{},{},{},{}}};
loop[[44]]={{"Q44",{2,(Subscript[2, 10]),22},0,"ca[44,21]",{11,4},{𝕓𝕒->𝕒10𝕓},{},{},{}},{"C44",{2.,(Subscript[2, 21])},0,"ca[44]",{44},{},{},{},{}},{"D44",{24,(Subscript[2, 10])},0,"ca[44,43]",{22,2},{𝕓𝕒->𝕒21𝕓},{},{},{}},
{"C22C2",{4.,(Subscript[4, 10])},0,"co[ca[11],C2C2]",{11,2,2},{},{},{},{}}};
loop[[45]]={{"C45",{1.,(Subscript[1, 44])},30,"ca[45]",{45},{},{18,23},{16,28},{17,23}},
{"C15C3",{1.,(Subscript[1, 44])},30,"co[ca[5],C3C3]",{15,3},{},{10,11,18},{8,12,16},{8,11,17}}};
loop[[46]]={{"C46",{2.,(Subscript[2, 22])},0,"ca[46]",{46},{},{},{},{}},{"D46",{24,(Subscript[1, 22])},0,"ca[46,45]",{23,2},{𝕓𝕒->𝕒22𝕓},{},{},{}}};
loop[[47]]={{"C47",{1.,(Subscript[1, 46])},0,"ca[47]",{47},{},{},{},{}}};

loop[[48]]={{"C3iC16",{2,(Subscript[2, 11]),(Subscript[6, 4])},0,"ca[48,41]",{3,16},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C48",{2.`,(Subscript[2, 23])},0,"ca[48]",{48},{},{},{},{}},{"C4C4iC3",{4,(Subscript[1, 32]),(Subscript[4, 3])},0,"ca[]",{3,2,2,2,2},{𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔𝕕,𝕔𝕒->𝕒𝕓𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕖𝕒->𝕒𝕕},{},{9,15},{10,12}},
{"C8S3",{8,(Subscript[2, 8]),(Subscript[8, 3])},33,"co[C8,S3]",{24,2},{𝕓𝕒->𝕒17𝕓},{},{},{}},{"C24jC2",{8,(Subscript[2, 8]),(Subscript[8, 3])},33,"ca[]",{2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕖𝕒->𝕒𝕖2},{},{},{}},{"C24iC2",{14,(Subscript[2, 10]),14},0,"co[ca[24,13],C2,2]",{24,2},{𝕓𝕒->𝕒11𝕓},{},{},{}},
{"D48",{26,(Subscript[2, 11])},0,"ca[48,47]",{24,2},{𝕓𝕒->𝕒23𝕓},{3,10,22},{},{4,8,22}},
{"Q48",{2,(Subscript[2, 10]),26},0,"ca[48,23]",{2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖2},{},{},{}},
{"C3iC8C2",{4,(Subscript[4, 5]),(Subscript[12, 2])},36,"co[ca[24,17],C2]",{3,8,2},{𝕓𝕒->𝕒2𝕓},{-11,35},{18,26},{}},
{"C3C8jC2",{4,(Subscript[4, 5]),(Subscript[12, 2])},36,"co[C3,co[ca[8],C2,4],2]",{3,8,2},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓5𝕔},{},{8,15,26},{}},

{"Q12C4",{4,(Subscript[4, 5]),(Subscript[12, 2])},36,"co[Q12,C4]",{12,4},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"Q12iC4",{4,(Subscript[4, 4]),12,16},0,"co[ca[12,5],C4,2]",{3,4,4},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓3𝕔},{},{},{}},{"C4iQ12",{4,(Subscript[4, 5]),24},0,"co[ca[4],ca[12,5],2]",{12,4},{𝕓𝕒->𝕒11𝕓},{10,13,16},{},{}},{"D12iC4",{16,(Subscript[4, 5]),12},0,"co[ca[12,11],C4,2]",{12,2,2},{𝕓𝕒->𝕒11𝕓𝕔},{9,15},{},{4,8,12}},{"C3iC8iC2",{18,(Subscript[2, 3]),(Subscript[6, 4])},0,"co[ca[24,17],C2,2]",{8,3,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒7𝕔},{},{},{}},{"C3iQ8iC2",{6,(Subscript[2, 2]),(Subscript[6, 4]),14},0,"co[C3,co[Q8,C2,2],2]",{3,8,2},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓3𝕔},{},{},{}},{"Q8iD6",{14,(Subscript[2, 2]),(Subscript[6, 5])},0,"co[Q8,ca[6,5],2]",{2,2,2,2,3},{𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖2,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"C3jQ16",{2,(Subscript[2, 2]),(Subscript[6, 4]),18},0,"ca[]",{2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖2,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},{"C2C2iQ12",{8,(Subscript[8, 2]),(Subscript[12, 2])},0,"co[C2C2,ca[12,5],2]",{6,4,2},{𝕓𝕒->𝕒5𝕓𝕔},{},{},{14,19}},
{"C12C4",{4.`,(Subscript[4, 11])},32,"co[C3,C4,C4,1]",{3,4,4},{},{10,12,16},{},{}},

{"C2C2iC12",{8,(Subscript[4, 6]),(Subscript[8, 2])},0,"co[C3,C2C2,C4,2]",{6,4,2},{𝕓𝕒->𝕒𝕓𝕔},{},{3,12,13},{2,8,12}},{"C4iC4iC3",{4,(Subscript[4, 5]),(Subscript[8, 3])},0,"co[co[C4,C4,2],C3,2]",{4,12},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"C24C2",{4.`,(Subscript[4, 11])},32,"co[ca[24],C2]",{24,2},{},{19,22},{17,25},{19,22}},{"C8jC2C3",{4,(Subscript[4, 11])},0,"co[co[ca[8],C2,4],C3]",{8,2,3},{𝕓𝕒->𝕒5𝕓},{2 𝕐,29},{22,25},{1,11,21}},{"C3D16",{10,(Subscript[2, 9]),(Subscript[10, 2])},0,"co[ca[16,15],C3]",{8,6},{𝕓𝕒->𝕒7𝕓},{22,32},{},{22,33}},
{"Q8iC6",{6,(Subscript[2, 6]),(Subscript[6, 5])},0,"co[Q8,C6,2]",{8,6},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"C3Q16",{2,(Subscript[2, 8]),(Subscript[10, 3])},0,"co[ca[16,7],C3]",{2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕓𝕔,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"S4iC2",{2,(Subscript[2, 14]),18},0,"ca[]",{2,3,2,2,2},{𝕒2->𝕖,𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕕,𝕔𝕓->𝕓𝕕𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕕𝕒->𝕒𝕔,𝕕𝕓->𝕓𝕔𝕕,𝕕𝕔->𝕔𝕕𝕖},{},{},{}},{"GL(2,3)",{14,(Subscript[2, 14]),6},0,"ca[]",{3,2,2,2,2},{𝕓𝕒->𝕒2𝕓,𝕔2->𝕖,𝕕2->𝕖,𝕔𝕓->𝕓𝕕,𝕔𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕔,𝕕𝕒->𝕒𝕔𝕕,𝕕𝕔->𝕔𝕕𝕖},{},{},{9,37},
"{{{1,2},{3,18},{4,9},{5,8},{6,10},{7,11},{12,33},{13,32},{14,34},{15,38},{16,24},{17,23},{19,26},{20,25},{21,27},{22,31},{28,48},{29,45},{30,44},{35,47},{36,41},{37,40},{39,46},{42,43}},{{1,3,11},{2,7,18},{4,30,47},{5,28,40},{6,14,27},{8,37,48},{9,35,44},{10,21,34},{12,41,31},{13,39,16},{15,29,26},{17,42,25},{19,45,38},{20,43,23},{22,36,33},{24,46,32}},{{1,4,6,16},{2,8,10,23},{3,12,14,29},{5,31,17,15},{7,19,21,36},{9,38,24,22},{11,25,27,40},{13,42,30,28},{18,32,34,44},{20,46,37,35},{26,47,41,39},{33,48,45,43}},{{1,5,6,17},{2,9,10,24},{3,13,14,30},{4,15,16,31},{7,20,21,37},{8,22,23,38},{11,26,27,41},{12,28,29,42},{18,33,34,45},{19,35,36,46},{25,39,40,47},{32,43,44,48}},{{1,6},{2,10},{3,14},{4,16},{5,17},{7,21},{8,23},{9,24},{11,27},{12,29},{13,30},{15,31},{18,34},{19,36},{20,37},{22,38},{25,40},{26,41},{28,42},{32,44},{33,45},{35,46},{39,47},{43,48}}}"},
{"A4iC4",{8,(Subscript[2, 8]),(Subscript[4, 3]),12},0,"ca[]",{2,2,3,2,2},
{𝕒2->𝕓,𝕔𝕒->𝕒𝕔2,𝕕𝕒->𝕒𝕖,𝕖𝕒->𝕒𝕕,𝕕𝕔->𝕔𝕖,𝕖𝕔->𝕔𝕕𝕖},{},{},{}},
{"C4A4",{8,(Subscript[2, 16]),8},37,"co[Transpose[A4],C4]",{3,2,2,4},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓},{},{4,46},{1,26}},
{"C2SL(2,3)",{4,(Subscript[4, 8]),12},0,"ca[]",{3,2,2,2,2},{𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔𝕕,𝕕𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},
{"SL(2,3)iC2",{8,(Subscript[2, 16]),8},37,"ca[]",{2,3,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕔𝕓->𝕓𝕔𝕕𝕖,𝕕𝕓->𝕓𝕔𝕖,𝕕𝕔->𝕔𝕕𝕖},{},{},{}},
{"Q24C2",{4,(Subscript[4, 4]),28},0,"co[ca[24,11],C2]",{6,2,2,2},{𝕓𝕒->𝕒5𝕓,𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{6,13,15},{1,8,15,18,36},{}},
{"C4D12",{16,(Subscript[4, 4]),16},35,"co[C4,S3,C2,1]",{12,2,2},{𝕓𝕒->𝕒5𝕓},{3,6,15},{},{}},
{"C2D24",{28,(Subscript[4, 5])},0,"co[ca[24,23],C2]",{12,2,2},{𝕓𝕒->𝕒11𝕓},{1,5,9},{2,15,18},{}},{"C12C2jC2"(*P48*),{16,(Subscript[4, 4]),16},35,"co[C3,P16a,2]",{},{},{2,3,5},{},{5,14,27}},{"D8S3",{24,(Subscript[2, 2]),(Subscript[6, 2]),8},0,"co[D8,S3]",{6,2,4},{𝕓𝕒->𝕒5𝕓,𝕔𝕒->𝕒𝕔3},{},{},{1,27,29}},
{"C2C3iC4iC2",{12,(Subscript[2, 2]),(Subscript[6, 2]),20},0,"co[C3,P16i,2]",{3,2,2,2,2},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕕𝕔->𝕔𝕕𝕖},{},{},{1,14,27}},{"Q8S3",{8,(Subscript[2, 2]),(Subscript[6, 2]),24},0,"co[Q8,S3]",{2,2,2,3,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕒𝕓𝕒𝕓->𝕔,𝕖𝕕->𝕕2𝕖},{},{},{14,27,30}},

{"Q8jS3",{20,(Subscript[2, 2]),(Subscript[6, 2]),12},0,"co[Q8,S3,4]",{2,2,2,2,3},{𝕓2->𝕕,𝕔2->𝕕,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖2,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"Q12C2C2",{8,(Subscript[8, 2]),24},0,"co[Q12,C2,C2,1]",{6,4,2},{𝕓𝕒->𝕒5𝕓},{6,13,19},{1,3,4,8,36},{}},
{"C2C2jD12",{20,(Subscript[8, 2]),12},0,"co[C2C2,ca[12,11],2]",{6,2,2,2},{𝕓𝕒->𝕒5𝕓𝕔},{2,3,19},{3,6,7},{3,6,19}},{"C12C2C2",{8.`,(Subscript[8, 5])},0,"co[C3,C4,C2,C2,1,1,1]",{3,4,2,2},{},{1,16,19},{3,15,17},{5,12,19}},
{"C6D8",{12,(Subscript[4, 3]),(Subscript[12, 2])},0,"co[C4,ca[12,7],2]",{12,2,2},{𝕓𝕒->𝕒7𝕓},{},{1,5,22},{1,5,27}},{"C6Q8",{4,(Subscript[4, 2]),(Subscript[12, 3])},0,"co[Q8,C3,C2,1]",{2,2,2,6},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{1,12,13,14},{}},{"C3C4C2kC2"(*PC3*),{8,(Subscript[8, 5])},0,"co[P16i,C3]",{2,2,6,2},{𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{2,12,15,19,36},{}},
{"C2S4",{20,(Subscript[2, 8]),(Subscript[4, 3])},0,"co[pe[s4],C2]",{3,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓,𝕕𝕒->𝕒2𝕕,𝕕𝕓->𝕔𝕕,𝕕𝕔->𝕓𝕕},{},{2,13},{2,18}},
{"C2C2A4",{16,(Subscript[4, 8])},0,"co[Transpose[A4],C2C2]",{3,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓},{},{},{1,18}},

{"C2C2C2C2iC3",{16,(Subscript[1, 32])},0,"ca[]",{3,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓,𝕕𝕒->𝕒𝕕𝕖,𝕖𝕒->𝕒𝕕},{},{3,10,35},{}},
{"C2C2C2S3",{32,(Subscript[8, 2])},0,"co[S3,C2C2C2]",{6,2,2,2},{𝕓𝕒->𝕒5𝕓},{1,3,6,19},{},{}},
{"C6C2C2C2",{16.`,(Subscript[16, 2])},0,"co[ca[6],C2C2,C2,1]",{6,2,2,2},{},{1,2,6,19},{1,2,3,22},{1,5,6,19}},{"OctC3",{2,(Subscript[2, 2]),(Subscript[14, 3])},0,"co[Oct,C3]",{},{},{},{},{}}};

loop[[49]]={{"C49",{1.,(Subscript[1, 48])},38,"ca[49]",{49},{},{},{},{}},{"C7C7",{1.,(Subscript[1, 48])},38,"co[ca[7],ca[7]]",{7,7},{},{},{},{}}};
loop[[50]]={{"D50",{26,(Subscript[1, 24])},40,"ca[50,49]",{25,2},{𝕓𝕒->𝕒24𝕓},{},{},{}},
{"C50",{2.,(Subscript[2, 24])},39,"ca[50]",{50},{},{},{},{}},{"C5iC10",{6,(Subscript[1, 20]),(Subscript[6, 4])},0,"co[ca[5],ca[10],2]",{5,10},{𝕓𝕒->𝕒4𝕓},{},{5,16},{2,17}},{"C5iD10",{26,(Subscript[1, 24])},40,"co[ca[5],ca[10,9],2]",{5,5,2},{𝕔𝕓->𝕓4𝕔,𝕔𝕒->𝕒4𝕔},{},{},{}},{"C10C5",{2.,(Subscript[2, 24])},39,"co[ca[10],ca[5]]",{10,5},{},{},{},{}}};
loop[[51]]={{"C51",{1.,(Subscript[1, 50])},0,"ca[51]",{51},{},{},{},{}}};

loop[[52]]={{"Q52",{2,(Subscript[2, 12]),26},0,"ca[52,25]",{13,4},{𝕓𝕒->𝕒12𝕓},{},{},{}},{"C52",{2.,(Subscript[2, 25])},0,"ca[52]",{52},{},{},{},{}},
{"C13iC4",{14,(Subscript[1, 12]),(Subscript[2, 13])},0,"ca[]",{13,4},{𝕓𝕒->𝕒5𝕓},{},{},{}},
{"D52",{28,(Subscript[2, 12])},0,"ca[52,51]",{26,2},{𝕓𝕒->𝕒25𝕓},{},{},{}},
{"C26C2",{4.,(Subscript[4, 12])},0,"co[ca[26],C2]",{26,2},{},{},{},{}}};
loop[[53]]={{"C53",{1.,(Subscript[1, 52])},0,"ca[53]",{53},{},{},{},{}}};

loop[[54]]={{"D54",{28,(Subscript[1, 26]),1},0,"ca[54,53]",{27,2},{𝕓𝕒->𝕒26𝕓},{},{},{}},
{"C54",{2.`,(Subscript[2, 26]),1},0,"ca[54]",{54},{},{},{},{}},{"C3D18",{10,(Subscript[1, 24]),(Subscript[10, 2]),4},0,"co[ca[18,17],C3]",{9,6},{𝕓𝕒->𝕒8𝕓},{23,32},{19,28},{}},{"C9S3",{4,(Subscript[1, 18]),(Subscript[4, 8]),4},0,"co[ca[9],S3]",{3,18},{𝕓𝕒->𝕒2𝕓},{7,10},{2,33},{3,23}},{"C3C3iC3iC2?",{10,(Subscript[1, 20]),(Subscript[4, 6]),4},0,"ca[]",{9,6},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C9iC3iC2?",{10,(Subscript[1, 20]),(Subscript[4, 6]),4},0,"ca[]",{2,3,3,3},{𝕔3->𝕕2,𝕔𝕒->𝕒𝕔2𝕕,𝕕𝕒->𝕒𝕕2,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},{"D18iC3",{28,(Subscript[1, 26]),4},0,"co[C3,ca[18,17],2]",{2,3,3,3},{𝕓3->𝕕2,𝕓𝕒->𝕒𝕓2𝕕,𝕔𝕒->𝕒𝕔2,𝕕𝕒->𝕒𝕕2},{3,10,23},{2,8,28},{}},
{"C3C3jC3kC2"(*P54*),{10,(Subscript[1, 24]),(Subscript[10, 2]),13},41,"ca[]",{2,3,3,3},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2,𝕔𝕓->𝕓𝕔𝕕},{},{2,5,7},{}},
{"C18C3",{2.`,(Subscript[2, 26]),4},0,"co[ca[18],C3]",{18,3},{},{19,23},{8,31},{19,23}},
{"Q54",{2,(Subscript[2, 26]),13},0,"co[P27,C2]",{6,3,3},{𝕓𝕒->𝕒𝕓𝕔},{},{8,20},{-8,10}},

{"C2C9iC3",{2,(Subscript[2, 26]),4},0,"ca[]",{9,6},{𝕓𝕒->𝕒4𝕓},{},{},{}},
{"C3C3S3",{4,(Subscript[1, 18]),(Subscript[4, 8]),13},0,"co[S3,C3,C3,0]",{3,6,3},{𝕓𝕒->𝕒2𝕓},{},{5,12,32},{2,8,11}},{"C3C3C3jC2",{10,(Subscript[1, 24]),(Subscript[10, 2]),13},41,"co[co[C3,ca[6,5],2],C3]",{2,3,3,3},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2},{},{5,7,32},{4,8,11}},
{"C3C3C3iC2",{28,(Subscript[1, 26]),13},0,"ca[]",{3,3,3,2},{𝕕𝕒->𝕒2𝕕,𝕕𝕓->𝕓2𝕕,𝕕𝕔->𝕔2𝕕},{},{},{}},{"C3C3C3",{2.`,(Subscript[2, 26]),13},0,"co[C3,C3,C3,C2,1]",{3,3,3,2},{},{10,11,19},{8,17,32},{8,11,19}}};
loop[[55]]={{"C11iC5",{1,(Subscript[1, 54])},0,"ca[]",{11,5},{𝕓𝕒->𝕒9𝕓},{},{},{}},{"C55",{1.,(Subscript[1, 54])},0,"ca[55]",{55},{},{},{},{}}};

loop[[56]]={{"C7iC8",{2,(Subscript[2, 13]),(Subscript[14, 2])},0,"ca[56,13]",{7,8},{𝕓𝕒->𝕒6𝕓},{21,35},{24,26},{}},
{"C56",{2.`,(Subscript[2, 27])},0,"ca[56]",{56},{},{21,22},{24,27},{20,22}},{"C7iQ8",{2,(Subscript[2, 12]),30},0,"co[ca[7],Q8,2]",{7,2,2,2},{𝕓2->𝕕,𝕔2->𝕕,𝕔𝕓->𝕓𝕔𝕕,𝕓𝕒->𝕒6𝕓},{13,14,21},{},{}},
{"Q56",{16,(Subscript[2, 12]),16},0,"co[ca[14,13],C4]",{28,2},{𝕓𝕒->𝕒13𝕓},{3,12,21},{},{}},
{"D56",{30,(Subscript[2, 13])},0,"ca[56,55]",{28,2},{𝕓𝕒->𝕒27𝕓},{3,4,21},{2,15,24},{}},
{"C2C7iC4",{4,(Subscript[4, 6]),28},0,"co[ca[14],C4,2]",{14,4},{𝕓𝕒->𝕒13𝕓},{6,13,21},{},{}},
{"C14C2iC2",{18,(Subscript[4, 6]),14},0,"co[C2C2,ca[14,13],2]",{7,4,2},{𝕓𝕒->𝕒6𝕓,𝕔𝕓->𝕓3𝕔},{2,3,21},{},{}},{"C28C2",{4.`,(Subscript[4, 13])},0,"co[ca[28],C2]",{28,2},{},{16,-21},{15,30},{12,-20}},
{"C7D8",{6,(Subscript[2, 7]),(Subscript[6, 6])},0,"ca[56,15]",{4,14},{𝕓𝕒->𝕒3𝕓},{},{},{2,5,20}},{"C7Q8",{2,(Subscript[2, 6]),(Subscript[6, 7])},0,"ca[56,43]",{2,2,2,7},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},

{"C2C2C2iC7",{8,(Subscript[1, 48])},0,"ca[]",{7,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕓},{},{},{}},{"C2C2D14",{32,(Subscript[4, 6])},0,"co[ca[14],C2C2,2]",{14,2,2},{𝕓𝕒->𝕒13𝕓},{3,6,-21},{2,3,30},{}},{"C14C2C2",{8.`,(Subscript[8, 6])},0,"co[ca[14],C2C2]",{14,2,2},{},{2,6,-21},{},{1,5,6,20}}};

loop[[57]]={{"C19iC3",{1,(Subscript[1, 56])},0,"ca[]",{19,3},{𝕓𝕒->𝕒7𝕓},{},{},{}},
{"C57",{1.,(Subscript[1, 56])},0,"ca[57]",{57},{},{},{},{}}};
loop[[58]]={{"D58",{30,(Subscript[1, 28])},0,"ca[58,57]",{29,2},{𝕓𝕒->𝕒28𝕓},{},{},{}},
{"C58",{2.,(Subscript[2, 28])},0,"ca[58]",{58},{},{},{},{}}};
loop[[59]]={{"C59",{1.,(Subscript[1, 58])},0,"ca[59]",{59},{},{},{},{}}};

loop[[60]]={{"C5C3iC4",{2,(Subscript[2, 14]),(Subscript[6, 5])},0,"co[C3,ca[20],2]",{3,4,5},{𝕓𝕒->𝕒2𝕓},{},{},{}},{"Q20C3",{2,(Subscript[2, 14]),(Subscript[10, 3])},0,"ca[60,49]",{5,4,3},{𝕓𝕒->𝕒4𝕓},{},{},{}},{"Q60",{2,(Subscript[2, 14]),30},0,"ca[60,29]",{15,4},{𝕓𝕒->𝕒14𝕓},{10,13,18},{},{}},{"C60",{2.`,(Subscript[2, 29])},0,"ca[60]",{5,4,3},{},{10,12,18},{8,15,16},{8,12,17}},{"A5",{16,(Subscript[1, 44])},0,"pe[\!\(\*TagBox[
RowBox[{"{", 
RowBox[{
RowBox[{"{", 
RowBox[{"5", ",", "3", ",", "4", ",", "1", ",", "2"}], "}"}], ",", 
RowBox[{"{", 
RowBox[{"5", ",", "1", ",", "3", ",", "4", ",", "2"}], "}"}]}], "}"}],
Short]\)]",{},{},{},{},{},{{{1,2,3,4,5},{1,2,3}}}},{"C3C5jC4",{6,(Subscript[1, 12]),(Subscript[2, 15]),(Subscript[6, 2])},0,"ca[]",{5,4,3},{𝕓𝕒->𝕒2𝕓},{},{},{}},{"C15jC4",{6,(Subscript[1, 12]),(Subscript[6, 7])},0,"ca[]",{15,4},{𝕓𝕒->𝕒8𝕓},{},{},{}},
{"S3D10",{24,(Subscript[1, 8]),(Subscript[4, 4]),(Subscript[6, 2])},0,"co[ca[30,19],C2,2]",{15,2,2},{𝕓𝕒->𝕒14𝕓,𝕔𝕒->𝕒4𝕔},{},{},{}},
{"C5A4",{4,(Subscript[1, 40]),(Subscript[4, 4])},0,"co[Transpose[A4],ca[5]]",{3,2,2,5},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓},{},{},{5,28}},{"C6D10",{12,(Subscript[2, 12]),(Subscript[12, 2])},0,"ca[60,19]",{5,6,2},{𝕓𝕒->𝕒4𝕓},{},{19,29},{}},{"C10S3",{8,(Subscript[2, 10]),(Subscript[8, 4])},0,"co[ca[6],ca[10],2]",{6,10},{𝕓𝕒->𝕒5𝕓},{},{},{3,-28}},{"D60",{32,(Subscript[2, 14])},0,"ca[60,59]",{30,2},{𝕓𝕒->𝕒29𝕓},{3,18,19},{2,8,29},{}},{"C30C2",{4.`,(Subscript[4, 14])},0,"co[ca[30],C2]",{5,3,2,2},{},{-18,19},{22,29},{19,25}}};

loop[[61]]={{"C61",{1.,(Subscript[1, 60])},0,"ca[61]",{61},{},{},{},{}}};
loop[[62]]={{"D62",{32,(Subscript[1, 30])},0,"ca[62,61]",{31,2},{𝕓𝕒->𝕒30𝕓},{},{},{}},{"C62",{2.,(Subscript[2, 30])},0,"ca[62]",{62},{},{},{},{}}};
loop[[63]]={{"C7iC9?",{1,(Subscript[1, 62])},0,"co[co[ca[7],C3,7],C3]",{7,3,3},{𝕓𝕒->𝕒2𝕓},{},{},{}},
{"C63",{1.,(Subscript[1, 62])},29,"ca[63]",{63},{},{21,23},{24,28},{20,23}},
{"C3C7iC3?",{1,(Subscript[1, 62])},0,"ca[]",{3,7,3},{𝕓𝕒->𝕒𝕓2},{},{},{}},
{"C21C3",{1.,(Subscript[1, 62])},29,"co[ca[7],C3C3]",{7,3,3},{},{10,11,21},{8,12,24},{8,11,20}}};

loop[[64]]={{"C64",{2.`,(Subscript[2, 31]),32,0},0,"ca[64]",{64},{},{},{},{}},{"g64002",{4.`,(Subscript[4, 15]),48,0},0,"co[C8,C8]",{8,8},{},{},{},{}},{"g64003",{4,(Subscript[4, 15]),48,1536},0,"co[C8,C8,4]",{8,8},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"g64004",{16,(Subscript[4, 8]),(Subscript[8, 2]),32,2688},0,"ca[]",{8,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕓𝕕},{},{},{}},{"g64005",{8,(Subscript[4, 8]),8,16,32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64006",{12,(Subscript[4, 6]),(Subscript[8, 2]),12,32,2304},0,"co[D8,ca[8,5],2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖},{29,17},{},{}},{"Q8pC8",{4,(Subscript[4, 5]),(Subscript[8, 2]),(Subscript[12, 2]),32,2304},0,"co[Q8,C8,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},{"g64008",{16,(Subscript[4, 4]),(Subscript[8, 4]),32,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},{"g64009",{8,(Subscript[4, 4]),(Subscript[8, 3]),16,40,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},

{"g64010",{12,(Subscript[4, 10]),12,32,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},
{"g64011",{4,(Subscript[4, 9]),(Subscript[12, 2]),32,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},
{"g64012",{20,(Subscript[4, 3]),(Subscript[8, 4]),32,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕗,𝕕2->𝕖𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},
{"g64013",{4,(Subscript[4, 2]),(Subscript[8, 4]),20,32,2880},47,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗,𝕕2->𝕖𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},
{"g64014",{4,(Subscript[4, 2]),(Subscript[8, 4]),20,32,2880},47,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕔2->𝕗,𝕕2->𝕖𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗},{},{},{}},
{"g64015",{4,(Subscript[4, 7]),(Subscript[8, 4]),48,2304},0,"co[ca[8,5],C8,2]",{8,8},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64016",{4,(Subscript[4, 7]),(Subscript[16, 2]),48,2304},0,"co[C8,C8,2]",{8,8},{𝕓𝕒->𝕒7𝕓},{29,22},{},{}},{"g64017",{8,(Subscript[8, 7]),32,1536},60,"co[C4C2,C8,4]",{8,4,2},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g64018",{8,(Subscript[8, 7]),40,2688},51,"ca[]",{4,4,4},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g64019",{8,(Subscript[8, 7]),48,2688},46,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},

{"g64020",{8,(Subscript[8, 7]),40,2304},0,"ca[]",{4,4,4},{𝕔𝕒->𝕓𝕔,𝕔𝕓->𝕒𝕔},{24,35},{},{}},{"g64021",{8,(Subscript[8, 3]),(Subscript[16, 2]),40,2304},52,"ca[]",{8,4,2},{𝕓𝕒->𝕒3𝕓𝕔},{},{},{}},{"g64022",{8,(Subscript[8, 7]),48,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64023",{16,(Subscript[8, 6]),48,2688},0,"ca[]",{4,4,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕},{},{},{}},{"g64024",{8,(Subscript[8, 5]),16,32,2688},0,"ca[]",{8,2,4},{𝕓𝕒->𝕒5𝕓,𝕔𝕒->𝕒𝕓𝕔},{},{},{}},{"g64025",{8,(Subscript[8, 7]),32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64026",{4.`,(Subscript[4, 15]),32,0},49,"co[C4,ca[16,9],4]",{16,4},{},{},{},{}},{"g64027",{4,(Subscript[4, 15]),32,1536},50,"ca[]",{16,4},{𝕓𝕒->𝕒9𝕓},{},{},{}},{"g64028",{4,(Subscript[4, 15]),32,2688},0,"ca[]",{16,4},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"g64029",{8,(Subscript[4, 8]),(Subscript[8, 3]),32,1536},0,"co[C2C2,ca[16],2]",{16,2,2},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},

{"g64030",{8,(Subscript[4, 8]),(Subscript[8, 3]),32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕕2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64031",{8,(Subscript[4, 8]),(Subscript[8, 3]),32,2304},0,"ca[]",{8,4,2},{𝕔𝕒->𝕒𝕓𝕔},{},{},{}},{"g64032",{20,(Subscript[4, 11]),28,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},{"g64033",{12,(Subscript[4, 10]),12,36,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64034",{20,(Subscript[4, 11]),44,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64035",{12,(Subscript[4, 10]),12,52,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{12,13}},
{"g64036",{12,(Subscript[4, 10]),12,32,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64037",{4,(Subscript[4, 10]),20,32,3264},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},{"g64038",{20,(Subscript[4, 7]),16,20,2688},0,"co[ca[16,15],C4,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64039",{4,(Subscript[4, 6]),16,20,36,2688},0,"co[ca[16,7],C4,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕔2->𝕖𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},

{"g64040",{12,(Subscript[4, 6]),(Subscript[8, 2]),12,24,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64041",{12,(Subscript[4, 6]),(Subscript[8, 2]),12,28,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64042",{20,(Subscript[4, 7]),(Subscript[8, 2]),24,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕔2->𝕖,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64043",{4,(Subscript[4, 6]),(Subscript[8, 2]),20,24,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕗,𝕔2->𝕖,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64044",{4,(Subscript[4, 7]),(Subscript[8, 4]),32,1536},0,"co[C4,ca[16],2]",{4,16},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64045",{4,(Subscript[4, 7]),(Subscript[8, 4]),32,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕔,𝕔2->𝕗,𝕕2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},{"g64046",{4,(Subscript[4, 7]),(Subscript[8, 4]),24,3072},0,"ca[]",{16,4},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64047",{4,(Subscript[4, 7]),32,36,2688},0,"co[ca[16],C4,2]",{16,4},{𝕓𝕒->𝕒15𝕓},{},{},{}},{"g64048",{4,(Subscript[4, 7]),(Subscript[16, 2]),36,2688},0,"ca[]",{16,4},{𝕓𝕒->𝕒7𝕓},{},{},{}},{"g64049",{4,(Subscript[4, 7]),(Subscript[16, 2]),40,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕔𝕖,𝕔2->𝕖𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},

{"g64050",{4.`,(Subscript[4, 15]),32,0},49,"co[ca[32],C2]",{32,2},{},{},{},{}},{"g64051",{4,(Subscript[4, 15]),32,1536},0,"ca[]",{32,2},{𝕓𝕒->𝕒17𝕓},{},{},{}},{"g64052",{34,(Subscript[2, 15]),33,2880},0,"ca[64,63]",{32,2},{𝕓𝕒->𝕒31𝕓},{},{},{}},{"g64053",{18,(Subscript[2, 14]),18,18,2880},0,"co[ca[32,15],C2,2]",{32,2},{𝕓𝕒->𝕒15𝕓},{},{},{}},{"g64054",{2,(Subscript[2, 14]),34,34,2880},0,"ca[64,31]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕔2->𝕕𝕖,𝕕2->𝕖𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕔𝕓->𝕓𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64055",{8.`,(Subscript[8, 7]),56,0},0,"co[C4,C4,C4,1]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕗},{},{},{}},
{"g64056",{16,(Subscript[16, 3]),48,1536},69,"co[C4C2,C4C2,4]",{4,4,2,2},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g64057",{8,(Subscript[8, 7]),56,1536},0,"ca[]",{4,4,4},{𝕓𝕒->𝕒𝕓𝕔2},{},{},{}},{"g64058",{16,(Subscript[8, 4]),16,48,1536},0,"co[C4,C2C2,C4,2]",{4,2,2,4},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g64059",{8,(Subscript[8, 3]),(Subscript[16, 2]),56,1536},0,"co[C4,C4,C4,2]",{4,4,4},{𝕓𝕒->𝕒3𝕓},{},{},{}},

{"g64060",{32,(Subscript[8, 4]),32,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64061?",{16,(Subscript[16, 3]),48,2304},0,"ca[]",{4,4,2,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},{"g64062",{16,(Subscript[8, 4]),16,48,2304},67,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64063",{8,(Subscript[8, 3]),(Subscript[16, 2]),56,2304},66,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"g64064",{8,(Subscript[8, 7]),56,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64065",{8,(Subscript[8, 3]),32,56,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"g64066",{16,(Subscript[8, 3]),24,48,2304},0,"co[C2C2,C4,C4,2,2]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64067",{24,(Subscript[8, 3]),16,40,2304},64,"co[C2C2,C2C2,C4,2,2]",{4,4,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒3𝕕},{},{},{}},
{"g64068",{8,(Subscript[8, 3]),(Subscript[16, 2]),56,2304},66,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"g64069",{16,(Subscript[8, 4]),16,48,2304},67,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕗,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},

{"g64070",{8,(Subscript[8, 2]),16,24,56,2304},65,"ca[]",{4,4,4},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔3},{},{},{}},{"g64071",{24,(Subscript[8, 3]),16,40,2304},64,"co[C4C2,D8,4]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕗,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"g64072",{8,(Subscript[8, 2]),16,24,56,2304},65,"co[C4C2,Q8,4]",{},{},{},{},{}},{"g64073",{32,(Subscript[8, 4]),32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},
{"g64074",{16,(Subscript[8, 3]),24,48,2688},63,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64075",{24,(Subscript[8, 3]),16,40,2688},0,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64076",{8,(Subscript[8, 3]),32,56,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64077",{16,(Subscript[16, 3]),48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕𝕖,𝕓2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64078",{16,(Subscript[8, 4]),16,48,2688},21,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64079",{8,(Subscript[8, 2]),16,24,56,2688},65,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},

{"g64080",{16,(Subscript[8, 3]),24,48,2688},63,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64081",{8,(Subscript[8, 3]),(Subscript[16, 2]),56,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64082",{8,(Subscript[8, 7]),56,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕𝕖𝕗,𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64083",{8.`,(Subscript[8, 7]),32,0},61,"co[C8,C4C2]",{8,4,2},{},{2,12,22},{1,15,27},{5,12,22}},{"g64084",{8,(Subscript[8, 7]),32,1536},60,"co[C8,C4C2,4]",{8,4,2},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"g64085",{8,(Subscript[8, 7]),32,1536},60,"co[C4,C8,C2,4]",{8,2,4},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"g64086",{8,(Subscript[8, 7]),32,1536},60,"ca[]",{2,4,8},{𝕓𝕒->𝕒𝕓𝕔4},{},{},{}},{"g64087",{16,(Subscript[8, 4]),16,32,1536},0,"co[C2C2,C8,C2,1,2]",{8,2,2,2},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g64088",{16,(Subscript[8, 4]),16,32,2304},59,"co[C2C2,C8,C2,4,2]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},
{"g64089",{16,(Subscript[8, 4]),16,32,2304},59,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},

{"g64090",{24,(Subscript[8, 5]),40,2688},0,"ca[]",{4,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕},{},{},{}},{"g64091",{16,(Subscript[8, 4]),16,48,2688},21,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{7,13,30}},{"g64092",{24,(Subscript[8, 5]),32,2688},0,"ca[]",{8,2,2,2},{𝕓𝕒->𝕒5𝕓,𝕔𝕒->𝕒𝕓𝕔},{},{},{}},{"g64093",{8,(Subscript[8, 4]),24,32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"g64094",{16,(Subscript[8, 4]),16,32,2688},100,"ca[]",{4,2,8},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔3},{},{},{},{},{}},
{"g64095",{24,(Subscript[8, 3]),16,24,2304},0,"co[C2,D8,C4,2]",{8,2,2,2},{𝕓𝕒->𝕒3𝕓𝕔},{},{},{}},{"g64096",{8,(Subscript[8, 2]),16,24,40,2304},0,"co[Q8,C4C2,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},{"g64097",{16,(Subscript[8, 4]),16,32,2304},59,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64098",{16,(Subscript[8, 2]),(Subscript[16, 2]),32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64099",{24,(Subscript[8, 5]),24,2688},72,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},

{"g64100",{8,(Subscript[8, 4]),24,40,2688},58,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64101",{16,(Subscript[8, 4]),16,32,2304},59,"ca[]",{2,2,4,4},{𝕔𝕒->𝕒𝕕3,𝕕𝕒->𝕒𝕔3},{24,26,29},{1,2,15,26},{5,7,12}},
{"g64102",{16,(Subscript[8, 4]),16,32,2688},100,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64103",{8,(Subscript[8, 3]),(Subscript[16, 2]),32,1536},28,"co[C2,C4,C8,2]",{4,8,2},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64104",{8,(Subscript[8, 3]),(Subscript[16, 2]),32,2304},28,"co[C4,C8,C2,4,2]",{8,2,4},{𝕓𝕒->𝕒5𝕓,𝕔𝕒->𝕒𝕔3},{},{},{}},
{"g64105",{8,(Subscript[8, 3]),(Subscript[16, 2]),32,2304},28,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64106",{8,(Subscript[8, 3]),(Subscript[16, 2]),40,2304},52,"co[ca[8,5],C4C2,2]",{8,4,2},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64107",{8,(Subscript[8, 3]),32,40,2304},0,"co[C8,C4C2,2]",{8,4,2},{𝕓𝕒->𝕒7𝕓},{6,13,17},{1,13,27},{1,16,22}},
{"g64108",{8,(Subscript[8, 3]),(Subscript[16, 2]),40,2304},52,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕕,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},{"g64109",{8,(Subscript[8, 4]),24,40,2688},58,"ca[]",{8,4,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒5𝕔},{},{},{}},
{"g64110",{8,(Subscript[8, 3]),(Subscript[16, 2]),48,2304},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕔,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},{"g64111",{8,(Subscript[8, 3]),(Subscript[16, 2]),48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g64112",{8,(Subscript[8, 7]),32,1536},60,"co[co[C2,C4],C8,4]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕},{},{},{}},
{"g64113",{8,(Subscript[8, 7]),32,2304},62,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},{"g64114",{8,(Subscript[8, 7]),32,2304},62,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64115",{12,(Subscript[4, 4]),(Subscript[12, 3]),32,1536},0,"co[D8,C8]",{4,2,8},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64116",{12,(Subscript[4, 4]),(Subscript[12, 3]),32,2304},34,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},{"g64117",{12,(Subscript[4, 4]),(Subscript[12, 3]),32,2304},34,"co[C8,D8,4]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},{"g64118",{20,(Subscript[4, 6]),20,28,2304},0,"co[C4,C8,C2,2]",{8,2,4},{𝕓𝕒->𝕒7𝕓},{4,12,22},{},{}},{"g64119",{12,(Subscript[4, 4]),(Subscript[12, 3]),36,2304},0,"co[C4,Q8,C2,2]",{8,2,4},{𝕓𝕒->𝕒3𝕓},{},{},{}},

{"g64120",{4,(Subscript[4, 5]),(Subscript[20, 2]),44,2304},0,"co[ca[16,7],C4]",{2,2,2,2,4},{𝕒2->𝕔,𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕓𝕕,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},{"g64121",{12,(Subscript[4, 5]),12,20,36,2688},0,"ca[]",{8,2,4},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒5𝕔},{},{},{}},{"g64122",{4,(Subscript[4, 4]),(Subscript[12, 2]),20,44,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕔2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64123",{20,(Subscript[4, 5]),(Subscript[12, 2]),28,2688},0,"ca[]",{8,2,4},{𝕓𝕒->𝕒7𝕓,𝕔𝕒->𝕒3𝕔},{},{},{}},{"g64124",{12,(Subscript[4, 4]),(Subscript[12, 3]),32,2304},34,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64125",{12,(Subscript[4, 4]),(Subscript[12, 3]),32,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"Q8C8",{4,(Subscript[4, 3]),(Subscript[12, 4]),32,1536},0,"co[Q8,C8]",{2,2,2,8},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"Q8pC8",{4,(Subscript[4, 3]),(Subscript[12, 4]),32,2304},0,"co[C8,Q8,4]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕕,𝕔2->𝕕𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},{"g64128",{32,(Subscript[4, 4]),(Subscript[8, 2]),31,2880},0,"co[C2C2,C8,C2,2,2]",{2,2,2,2,2,2},{𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64129",{16,(Subscript[4, 4]),8,24,32,2880},70,"co[Q8,C2C2,C2,2,2]",{},{},{},{},{}},

{"g64130",{24,(Subscript[4, 4]),8,16,24,2880},71,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64131",{24,(Subscript[4, 4]),8,16,24,2880},71,"co[C2C2,Q8,C2,2,2]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},{"g64132",{8,(Subscript[4, 4]),8,32,40,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64133",{16,(Subscript[4, 4]),8,24,32,2880},70,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗},{},{},{}},
{"g64134",{28,(Subscript[4, 6]),12,27,3072},54,"ca[]",{2,2,2,2,2,2},{𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64135",{20,(Subscript[4, 6]),20,28,3072},53,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64136",{20,(Subscript[4, 6]),20,28,3072},53,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64137",{12,(Subscript[4, 6]),28,36,3072},73,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕕𝕓->𝕓𝕕𝕗,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},
{"g64138",{28,(Subscript[4, 6]),12,36,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{1,3,4}},
{"g64139",{20,(Subscript[4, 6]),20,44,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{5,13,30}},

{"D8iD8",{28,(Subscript[4, 2]),(Subscript[8, 2]),12,27,2880},0,"co[D8,D8,2]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},{"Q8pD8?",{20,4,(Subscript[8, 2]),(Subscript[12, 2]),28,2880},0,"co[Q8,D6,2]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64142",{12,4,(Subscript[8, 2]),12,20,36,2880},74,"co[C4,Q8,C2,2,2]",{8,2,4},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔3},{},{},{}},
{"g64143?",{4,4,(Subscript[8, 2]),12,28,44,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64144?",{20,4,(Subscript[8, 2]),(Subscript[12, 2]),28,2880},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},{"g64145",{12,4,(Subscript[8, 2]),12,20,36,2880},74,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕𝕗,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64146",{16,(Subscript[8, 4]),16,32,2688},100,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},{"g64147",{24,(Subscript[8, 3]),16,24,2688},0,"co[C8,C4,C2,2,2]",{4,2,8},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔7},{2,3,22},{},{}},
{"g64148",{8,(Subscript[8, 2]),16,24,40,2688},0,"co[C2C2,ca[16,7],2]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g64149",{16,(Subscript[8, 2]),(Subscript[16, 2]),32,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},

{"g64150",{24,(Subscript[8, 5]),24,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},{"g64151",{8,(Subscript[8, 4]),24,40,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g64152",{16,(Subscript[8, 4]),16,32,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64153",{24,(Subscript[8, 5]),32,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64154",{8,(Subscript[8, 4]),24,32,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"D8iQ8",{12,(Subscript[4, 2]),(Subscript[8, 2]),28,36,2880},0,"co[D8,Q8,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"Q8pQ8",{4,(Subscript[8, 2]),(Subscript[12, 2]),20,44,2880},75,"co[Q8,Q8,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64157",{12,4,(Subscript[8, 2]),12,20,36,2880},74,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕𝕗,𝕓2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64158?",{4,4,(Subscript[8, 2]),12,28,44,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕𝕗,𝕓2->𝕕,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64159",{12,4,(Subscript[8, 2]),12,20,36,2880},74,"ca[]",{2,2,2,2,2,2},{"𝕒2"->"𝕕","𝕓2"->"𝕕𝕗","𝕖2"->"𝕗","𝕓𝕒"->"𝕒𝕓𝕕","𝕔𝕒"->"𝕒𝕔𝕖","𝕖𝕒"->"𝕒𝕖𝕗","𝕖𝕔"->"𝕔𝕖𝕗"},{},{},{}},

{"g64160",{4,(Subscript[8, 2]),(Subscript[12, 2]),20,44,2880},75,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕𝕗,𝕔2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64161",{16,(Subscript[4, 4]),8,24,32,2880},70,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},{"g64162",{16,(Subscript[4, 4]),(Subscript[8, 2]),16,32,2880},76,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕕𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},{"g64163",{16,(Subscript[4, 4]),(Subscript[8, 2]),16,32,2880},76,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64164",{8,(Subscript[4, 4]),8,(Subscript[16, 2]),40,2880},77,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64165",{8,(Subscript[4, 4]),16,24,40,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕕𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64166",{8,(Subscript[4, 4]),8,(Subscript[16, 2]),40,2880},77,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕔2->𝕕,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕔->𝕔𝕖𝕗},{},{},{}},
{"g64167",{20,(Subscript[4, 6]),20,28,2688},57,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64168",{4,(Subscript[4, 5]),(Subscript[20, 2]),44,2688},78,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},{"g64169",{12,(Subscript[4, 4]),(Subscript[12, 3]),36,2688},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖𝕗,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},


{"g64170",{12,(Subscript[4, 5]),12,20,36,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64171",{20,(Subscript[4, 5]),(Subscript[12, 2]),28,3072},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖𝕗,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},{"g64172",{4,(Subscript[4, 4]),(Subscript[12, 2]),20,44,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖𝕗,𝕔2->𝕕,𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},{"g64173",{20,(Subscript[4, 6]),20,28,2688},57,"ca[]",{4,8,2},{𝕔𝕒->𝕒3𝕔,𝕔𝕓->𝕓3𝕔},{},{},{}},{"g64174",{36,(Subscript[4, 7]),35,2688},79,"co[C4,ca[16,15],2]",{4,8,2},{𝕔𝕒->𝕒3𝕔,𝕔𝕓->𝕓7𝕔},{3,16,22},{},{}},
{"g64175?",{4,(Subscript[4, 6]),36,44,2688},0,"co[C4,ca[16,7],2]",{},{},{},{},{}},{"g64176",{20,(Subscript[4, 6]),20,28,2688},57,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕔2->𝕖𝕗,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},{"g64177",{28,(Subscript[4, 6]),12,27,3072},54,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕,𝕔2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g64178",{12,(Subscript[4, 6]),28,36,3072},73,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕕,𝕔2->𝕖,𝕕2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g64179",{4,(Subscript[4, 5]),(Subscript[20, 2]),44,2688},78,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},

{"g64180",{4,(Subscript[4, 5]),(Subscript[20, 2]),44,2688},78,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕𝕗,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64181?",{4,(Subscript[4, 6]),36,44,2688},0,"co[C8,Q8,2]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕖𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕖𝕒->𝕒𝕖𝕗},{13,14,17},{13,14,27},{}},
{"g64182",{4,(Subscript[4, 5]),12,28,44,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕔2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕗,𝕖𝕒->𝕒𝕖𝕗},{},{},{}},
{"g64183",{8.,(Subscript[8, 7]),32,0},61,"co[C2C2,ca[16],4]",{2,2,16},{},{},{},{}},{"g64184",{8,(Subscript[8, 7]),32,1536},60,"ca[]",{16,2,2},{𝕓𝕒->𝕒9𝕓},{},{},{}},{"g64185",{8,(Subscript[8, 7]),32,1536},60,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕕2->𝕖,𝕖2->𝕗,𝕔𝕓->𝕓𝕔𝕗},{},{},{}},
{"g64186",{36,(Subscript[4, 7]),35,2688},79,"co[ca[32,31],C2]",{16,2,2},{𝕓𝕒->𝕒15𝕓},{},{},{}},{"g64187",{20,(Subscript[4, 6]),20,20,2688},81,"co[ca[16,9],C2C2,2]",{16,2,2},{𝕓𝕒->𝕒7𝕓},{},{},{}},{"g64188",{4,(Subscript[4, 6]),36,36,2688},0,"co[ca[32,15],C2]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},
{"g64189",{20,(Subscript[4, 6]),20,20,2688},81,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕗,𝕕2->𝕖𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},

{"g64190",{28,(Subscript[4, 6]),12,27,3072},54,"ca[]",{16,2,2},{𝕓𝕒->𝕒15𝕓,𝕔𝕒->𝕒7𝕔},{},{},{}},{"g64191",{12,(Subscript[4, 6]),28,28,3072},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕔𝕓->𝕓𝕔𝕕,𝕗2->𝕖,𝕗𝕒->𝕒𝕗𝕖},{},{},{}},{"g64192",{16.`,(Subscript[16, 3]),48,0},0,"co[C4C2,C4C2]",{2,2,4,4},{},{},{},{}},{"g64193",{32,(Subscript[16, 2]),32,1536},0,"co[C2C2,C2C2,C4,2]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔𝕒->𝕒𝕓𝕔𝕖},{},{},{}},
{"g64194",{16,16,32,48,1536},0,"co[C2C2,C4,C4,2]",{4,4,2,2},{𝕓𝕒->𝕒3𝕓},{6,8,13,16},{},{}},
{"g64195",{16,(Subscript[16, 3]),48,1536},69,"co[C2,co[C2,C4],C4,4]",{4,2,4,2},{𝕓𝕒->𝕒𝕓𝕔2},{},{},{}},
{"g64196",{24,(Subscript[8, 2]),24,40,1536},0,"co[C4C2,D8]",{4,2,4,2},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"Q8C4C2",{8,8,(Subscript[24, 2]),56,1536},0,"co[Q8,C4C2]",{2,2,2,4,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"g64198",{16,(Subscript[16, 3]),48,1536},69,"co[C4,D8,C2,4]",{2,2,2,2,4},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕔𝕕},{},{},{}},
{"g64199",{24,8,(Subscript[16, 2]),40,1920},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},

{"g64200",{8,(Subscript[16, 2]),24,56,1920},0,"ca[]",{2,2,2,2,4},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕖𝕕->𝕔𝕕𝕖},{},{},{}},
{"g64201",{16,8,16,24,48,1920},0,"ca[]",{2,2,2,2,4},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕔𝕕,𝕖𝕕->𝕔𝕕𝕖},{},{},{}},{"g64202",{40,(Subscript[8, 3]),39,2304},82,"ca[]",{4,2,2,2,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔𝕕},{},{1,3,4,5,34},{}},
{"g64203",{32,(Subscript[16, 2]),32,2304},0,"co[C2,C2C2,D8,2,2]",{4,2,4,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒𝕔3},{2,4,6,16},{},{}},
{"g64204",{16,16,32,48,2304},0,"co[C2C2,co[Q8,C2],2]",{2,2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕𝕖},{},{1,3,4,13,14},{}},
{"g64205?",{24,(Subscript[8, 2]),24,40,2304},0,"co[C4,co[P4,C4],2]",{2,2,2,2,2,2},{"𝕔2"->"𝕖","𝕓𝕒"->"𝕒𝕓𝕖","𝕔𝕒"->"𝕒𝕔𝕗"},{2,13,14,16},{},{1,2,7,30}},
{"g64206?",{24,(Subscript[8, 2]),24,40,2304},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64207?",{24,(Subscript[8, 2]),24,40,2304},0,"co[C2C2,Q8,C2,4,2]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},
{"g64208",{8,8,(Subscript[24, 2]),56,2304},84,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},{"g64209?",{16,(Subscript[16, 3]),48,2304},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕕𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},

{"g64210?",{16,(Subscript[16, 3]),48,2304},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},
{"g64211",{40,(Subscript[8, 3]),39,2304},82,"co[C2,C4,D8,2]",{4,4,2,2},{𝕔𝕓->𝕓3𝕔,𝕔𝕒->𝕒3𝕔},{},{},{}},
{"g64212",{8,(Subscript[8, 2]),40,56,2304},0,"co[C2,C4,Q8,2]",{4,2,2,2,2},{𝕓𝕒->𝕒3𝕓,𝕓2->𝕔,𝕕2->𝕔,𝕕𝕓->𝕓𝕔𝕕},{8,13,14,16},{},{}},{"g64213?",{24,(Subscript[8, 2]),24,40,2304},0,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗},{},{},{}},
{"g64214",{8,8,(Subscript[24, 2]),56,2304},84,"co[co[C2,C4],Q8,4]",{2,2,2,2,2,2},{𝕒2->𝕕,𝕓2->𝕖,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖},{},{},{}},
{"g64215",{32,(Subscript[8, 2]),16,32,2688},85,"ca[]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},
{"g64216",{32,(Subscript[8, 2]),16,32,2688},85,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64217",{16,(Subscript[8, 2]),32,48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64218",{24,16,24,40,2688},0,"ca[]",{2,2,2,2,2,2},{𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64219",{24,8,(Subscript[16, 2]),40,2688},87,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},

{"g64220?",{16,8,16,24,48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64221",{24,8,(Subscript[16, 2]),40,2688},87,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64222",{8,(Subscript[16, 2]),24,56,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},
{"g64223?",{16,8,16,24,48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},{"g64224",{16,(Subscript[24, 2]),48,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},
{"g64225",{8,8,16,32,56,2688},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖},{},{},{}},
{"D8D8",{36,4,(Subscript[12, 2]),35,2496},0,"co[D8,D8]",{4,2,4,2},{𝕓𝕒->𝕒3𝕓,𝕕𝕔->𝕔3𝕕},{},{},{}},
{"g64227",{28,4,12,20,36,2496},86,"co[C2C2,P16i,2]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"g64228",{20,4,12,28,44,2496},88,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"D8pD8",{20,4,12,28,44,2496},88,"co[D8,D8,4]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},

{"Q8D8",{12,4,12,36,52,2496},0,"co[Q8,D8]",{2,2,2,4,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕖𝕕->𝕕3𝕖},{},{},{}},
{"g64231",{28,4,12,20,36,2496},86,"co[Q8,D8,4]",{2,2,2,2,2,2},{𝕓2->𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64232?",{20,(Subscript[12, 2]),20,44,2496},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64233?",{12,12,(Subscript[20, 2]),52,2496},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64234?",{20,(Subscript[12, 2]),20,44,2496},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64235",{12,4,20,28,52,2496},0,"co[D8,Q8,4]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64236?",{20,(Subscript[12, 2]),20,44,2496},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64237?",{12,12,(Subscript[20, 2]),52,2496},0,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕖𝕗,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"Q8pQ8",{4,12,20,28,60,2496},0,"co[Q8,Q8,4]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖,𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"Q8Q8",{4,(Subscript[12, 2]),36,60,2496},0,"co[Q8,Q8]",{2,2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕2->𝕗,𝕖2->𝕗,𝕖𝕕->𝕕𝕖𝕗},{},{},{}},

{"g64240?",{20,(Subscript[12, 2]),20,44,2496},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕖𝕗,𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"g64241",{28,(Subscript[12, 3]),36,2880},90,"ca[]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕒->𝕒𝕕𝕖𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64242",{28,(Subscript[12, 3]),36,2880},90,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕒->𝕒𝕕𝕖𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"g64243",{20,4,(Subscript[20, 2]),44,2880},0,"ca[]",{2,2,2,2,2,2},{𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕒->𝕒𝕕𝕖𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64244",{12,(Subscript[12, 2]),28,52,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕖,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕒->𝕒𝕕𝕖𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},
{"g64245",{4,(Subscript[20, 3]),60,2880},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕓2->𝕗,𝕔2->𝕗,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕔𝕓->𝕓𝕔𝕖𝕗,𝕕𝕒->𝕒𝕕𝕖𝕗,𝕕𝕓->𝕓𝕕𝕖},{},{},{}},{"g64246",{16.,(Subscript[16, 3]),32,0},0,"co[C8,C2C2,C2,1]",{2,2,2,8},{},{2,6,8,22},{},{}},{"g64247",{16,(Subscript[16, 3]),32,1536},91,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕗},{},{},{}},
{"g64248",{16,(Subscript[16, 3]),32,1536},91,"co[C2,C8,C2C2,4]",{8,2,2,2},{𝕓𝕒->𝕒5𝕓},{},{},{}},{"g64249",{16,(Subscript[16, 3]),32,1920},0,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕖2->𝕗,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},

{"g64250",{40,(Subscript[8, 3]),39,2304},82,"co[C2,D8,C2C2,2]",{8,2,2,2},{𝕓𝕒->𝕒7𝕓},{6,8,9,22},{},{}},{"g64251",{24,(Subscript[8, 2]),24,24,2304},92,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64252",{8,(Subscript[8, 2]),40,40,2304},0,"co[ca[16,7],C2C2]",{2,2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕓𝕕,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},{"g64253",{24,(Subscript[8, 2]),24,24,2304},92,"co[C2,Q8,C2C2,2]",{8,2,2,2},{𝕓𝕒->𝕒3𝕓},{},{},{}},{"g64254",{32,(Subscript[8, 2]),16,31,2688},93,"ca[]",{8,2,2,2},{𝕓𝕒->𝕒3𝕓,𝕔𝕒->𝕒5𝕔},{},{},{}},{"g64255",{16,(Subscript[8, 2]),32,32,2688},95,"ca[]",{2,2,2,2,2,2},{𝕓2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64256",{24,(Subscript[8, 2]),24,24,2688},94,"ca[]",{2,2,2,2,2,2},{𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64257",{32,(Subscript[8, 2]),16,31,2688},93,"ca[]",{2,2,2,2,2,2},{𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64258",{24,(Subscript[8, 2]),24,24,2688},94,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g64259",{16,(Subscript[8, 2]),32,32,2688},95,"ca[]",{2,2,2,2,2,2},{𝕒2->𝕗,𝕓2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕓𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕖𝕗,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},

{"g64260",{32.`,32,32,0},0,"co[C4C2,C2C2C2]",{2,2,2,2,4},{},{1,2,6,8,16},{},{}},{"g64261",{48,16,47,1536},0,"co[D8,C2C2C2]",{4,2,2,2,2},{𝕓𝕒->𝕒3𝕓},{1,3,6,8,9},{},{}},{"g64262",{16,48,48,1536},0,"co[Q8,C2C2C2]",{2,2,2,2,2,2},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"g64263",{32,32,32,1536},0,"co[C2C2,D8,C2,4]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕗𝕕->𝕕𝕖𝕗},{2,3,4,6,8},{1,2,3,15,36},{}},{"CL32C2",{40,24,39,1920},0,"co[cLoop[3.,2],C2]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕔,𝕖𝕕->𝕔𝕕𝕖},{},{},{}},{"CL5C2",{24,40,40,1920},0,"co[cLoop[5.],C2]",{2,2,2,2,2,2},{𝕓𝕒->𝕒𝕓𝕖,𝕔𝕒->𝕒𝕔𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕕𝕔->𝕔𝕕𝕖},{},{},{}},{"CL41C2",{32,32,32,1920},0,"co[cLoop[4.,1],C2]",{2,2,2,2,2,2},{𝕒2->𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕗𝕕->𝕕𝕖𝕗},{},{},{}},
{"C2C2C2C2C2",{64.,63,0},0,"co[C2,co[C2,co[C2,co[C2,co[C2,C2]]]]]",{2,2,2,2,2,2},{},{},{},{}},
{"CL60",{-36,28,36,2016},0,"cLoop[6.]",{},{},{},{},{}},
{"CL51?",{-36,28,36,2016},0,"cLoop[5.,1]",{},{},{},{},{}},{"CL42",{-28,36,35,2016},0,"cLoop[4.,2]",{},{},{},{},{}},
{"CL33?",{-28,36,35,2016},0,"cLoop[3.,3]",{},{},{},{},{}},
{"CL24?",{-36,28,36,2016},0,"cLoop[2.,4]",{},{},{},{},{}},
{"CL15?",{-36,28,36,2016},0,"cLoop[1.,5]",{},{},{},{},{}},
{"CL06?",{-28,36,35,2016},0,"cLoop[0.,6]",{},{},{},{},{}},{"OctC4",{4,4,(Subscript[28, 2]),60,2688},0,"co[Oct,C4]",{},{},{},{},{}},{"OctiC4n",{4,(Subscript[4, 2]),(Subscript[8, 3]),28,36,3008},0,"co[Oct,C4,2]",{},{},{},{},{}},
{"OctK",{8,56,56,2688},0,"co[Oct,C2C2]",{},{},{},{},{}},{"OctiKn",{12,(Subscript[4, 2]),(Subscript[8, 2]),28,28,3008},0,"co[Oct,C2C2,2]",{},{},{},{},{}}};

loop[[65]]={{"C65",{1.,(Subscript[1, 64])},0,"ca[65]",{13,5},{},{},{},{}}};
loop[[66]]={{"C11S3",{4,(Subscript[1, 22]),(Subscript[4, 10])},0,"ca[66,23]",{3,2,11},{𝕓𝕒->𝕒2𝕓},{},{},{}},{"C3D22",{12,(Subscript[1, 30]),(Subscript[12, 2])},0,"ca[66,43]",{11,2,3},{𝕓𝕒->𝕒10𝕓},{},{},{}},{"D66",{34,(Subscript[1, 32])},0,"ca[66,65]",{33,2},{𝕓𝕒->𝕒32𝕓},{},{},{}},
{"C66",{2.,(Subscript[2, 32])},0,"ca[66]",{66},{},{},{},{}}};
loop[[67]]={{"C67",{1.,(Subscript[1, 66])},0,"ca[67]",{67},{},{},{},{}}};
loop[[68]]={{"Q68",{2,(Subscript[2, 16]),34},0,"ca[68,33]",{17,4},{𝕓𝕒->𝕒16𝕓},{},{},{}},{"C68",{2.,(Subscript[2, 33])},0,"ca[68]",{68},{},{},{},{}},
{"C17jC4",{18,(Subscript[1, 16]),(Subscript[2, 17])},0,"ca[]",{2,2,17},{𝕒2->𝕓𝕔,𝕔𝕒->𝕒𝕔13,𝕔𝕓->𝕓𝕔16},{},{},{}},{"D68",{36,(Subscript[2, 16])},0,"ca[68,67]",{34,2},{𝕓𝕒->𝕒33𝕓},{},{},{}},
{"C34C2",{4.,(Subscript[4, 16])},0,"ca[68,35]",{17,2,2},{},{},{},{}}};
loop[[69]]={{"g6901",{1.,(Subscript[1, 68])},0,"ca[69]",{69},{},{},{},{}}};
loop[[70]]={{"C7D10",{6,(Subscript[1, 28]),(Subscript[6, 6])},0,"ca[70,29]",{},{},{},{},{}},
{"C5D14",{8,(Subscript[1, 30]),(Subscript[8, 4])},0,"ca[70,41]",{},{},{},{},{}},
{"D70",{36,(Subscript[1, 34])},0,"ca[70,69]",{},{},{3,18,21},{2,16,24},{}},
{"C70",{2.,(Subscript[2, 34])},0,"ca[70]",{70},{},{-18,21},{16,30},{20,25}}};
loop[[71]]={{"C71",{1.,(Subscript[1, 70])},0,"ca[71]",{},{},{},{},{}}};

loop[[72]]={{"g7201",{2,(Subscript[2, 17]),(Subscript[18, 2]),1},0,"ca[72,53]",{2,2,2,3,3},{𝕒2->𝕓,𝕓2->𝕔,𝕕3->𝕖2,𝕕𝕒->𝕒𝕕2𝕖,𝕖𝕒->𝕒𝕖2},{23,35},{26,28},{}},
{"C72",{2.`,(Subscript[2, 35]),1},0,"ca[72]",{9,8},{},{22,23},{25,33},{22,23}},{"g7203",{2,(Subscript[2, 26]),(Subscript[6, 3]),1},0,"ca[]",{9,2,2,2},{𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔𝕕,𝕕𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},
{"Q72",{2,(Subscript[2, 16]),38,1},0,"ca[72,35]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕕3->𝕖2,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕2𝕖,𝕖𝕒->𝕒𝕖2},{13,14,23},{},{}},
{"D18C4",{20,(Subscript[2, 16]),20,1},0,"co[ca[18,17],C4,2]",{9,2,4},{𝕓𝕒->𝕒8𝕓},{3,12,23},{},{}},
{"D72",{38,(Subscript[2, 17]),1},0,"ca[72,71]",{36,2},{𝕓𝕒->𝕒35𝕓},{3,4,23},{2,15,28},{}},
{"Q36C2",{4,(Subscript[4, 8]),36,1},0,"co[ca[36,17],C2]",{9,4,2},{𝕓𝕒->𝕒8𝕓},{6,13,23},{},{}},
{"KnD18",{22,(Subscript[4, 8]),18,1},0,"co[ca[36,17],C2,2]",{18,2,2},{𝕓𝕒->𝕒17𝕓𝕔},{2,3,23},{},{}},
{"C9C4C2",{4.,(Subscript[4, 17]),1},0,"co[ca[36],C2]",{9,4,2},{},{7,12},{15,31},{12,-23}},
{"D8C9",{6,(Subscript[2, 9]),(Subscript[6, 8]),1},0,"ca[72,7]",{4,2,9},{𝕓𝕒->𝕒3𝕓},{2,7},{3,5,33},{}},

{"Q8C9",{2,(Subscript[2, 8]),(Subscript[6, 9]),1},0,"ca[72,19]",{2,2,2,9},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g7212",{2,(Subscript[2, 17]),(Subscript[6, 6]),4},0,"co[ca[3],ca[8],ca[3],3]",{3,24},{𝕓𝕒->𝕒2𝕓},{},{8,25},{8,21}},{"C3^2nC8",{2,(Subscript[2, 17]),(Subscript[18, 2]),4},0,"co[C3,ca[24,5],2]",{3,3,8},{𝕔𝕓->𝕓2𝕔,𝕔𝕒->𝕒2𝕔},{},{8,26,32},{}},{"C8C3^2",{2.,(Subscript[2, 35]),4},0,"co[ca[24],C3]",{8,3,3},{},{10,11,22},{8,12,27},{8,11,22}},
{"g7215",{22,(Subscript[1, 24]),(Subscript[4, 2]),(Subscript[6, 3]),1},0,"ca[]",{2,3,3,2,2},{𝕓3->𝕔2,𝕓𝕒->𝕒𝕓2𝕔,𝕔𝕒->𝕒𝕔2,𝕕𝕒->𝕒𝕖,𝕕𝕓->𝕓𝕖,𝕖𝕒->𝕒𝕕,𝕖𝕓->𝕓𝕕𝕖},{},{},{}},
{"g3603C2?",{8,(Subscript[2, 24]),(Subscript[8, 2]),1},0,"ca[]",{3,3,2,2,2},{"𝕒3"->𝕓,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕔},{},{},{}},{"D18K",{40,(Subscript[4, 8]),1},0,"co[ca[18,17],C2C2]",{9,2,2,2},{𝕓𝕒->𝕒8𝕓},{3,6,-23},{2,3,31},{}},{"C9C2^3",{8.,(Subscript[8, 8]),1},0,"co[C2,ca[36,19]]",{9,2,2,2},{},{2,6,-23},{},{1,5,6,23}},
{"g7219",{2,(Subscript[2, 26]),18,4},0,"ca[]",{8,3,3},{𝕓𝕒->𝕒𝕔2,𝕔𝕒->𝕒𝕓},{},{},{}},
{"Q12D3",{8,(Subscript[2, 6]),(Subscript[6, 2]),(Subscript[8, 2]),24,4},0,"co[ca[12,5],S3]",{3,2,3,4},{𝕓𝕒->𝕒2𝕓,𝕕𝕔->𝕔2𝕕},{},{},{16,27}},

{"g7221",{20,(Subscript[2, 8]),(Subscript[6, 4]),12,4},0,"co[C3,co[ca[6,5],C4,2],2]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕕𝕓->𝕓𝕕2,𝕖𝕒->𝕒𝕖2},{},{},{4,27}},{"g7222",{14,(Subscript[2, 4]),(Subscript[8, 4]),18,4},0,"ca[]",{2,2,2,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕕2,𝕖𝕒->𝕒𝕖2},{},{},{7,8,16}},{"Q12nD3",{26,(Subscript[2, 6]),(Subscript[6, 3]),(Subscript[8, 2]),4},0,"co[ca[12,5],S3,2]
    ",{12,3,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒11𝕔},{},{},{4,7,8}},{"g7224",{2,(Subscript[2, 8]),(Subscript[6, 4]),30,4},0,"ca[]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕕2,𝕖𝕒->𝕒𝕖2},{},{},{8,15,16}},
{"SL23C3",{2,(Subscript[2, 26]),(Subscript[6, 3]),13},0,"ca[]",{3,2,2,2,3},{𝕓2->𝕔,𝕕2->𝕔,𝕓𝕒->𝕒𝕓𝕔𝕕,𝕕𝕒->𝕒𝕓𝕔,𝕕𝕓->𝕓𝕔𝕕},{},{},{}},{"Q24C3",{2,(Subscript[2, 14]),(Subscript[14, 3]),4},0,"co[ca[24,11],C3]",{3,2,2,2,3},{𝕓𝕒->𝕒2𝕓,𝕓2->𝕕,𝕔2->𝕕,𝕔𝕓->𝕓𝕔𝕕},{},{8,13,14},{8,14,30}},{"D3C3C4",{8,(Subscript[2, 12]),(Subscript[8, 5]),4},0,"co[S3,C3,C4,1]",{3,6,4},{𝕓𝕒->𝕒2𝕓},{13,32},{7,46},{}},
{"C4iD3C3",{14,(Subscript[2, 15]),(Subscript[14, 2]),4},0,"co[co[C4,S3,2],C3]",{12,2,3},{𝕓𝕒->𝕒11𝕓},{3,32},{8,15,19},{8,39,40}},{"Q12C6",{4,(Subscript[4, 8]),(Subscript[12, 3]),4},0,"co[ca[12,5],C6]",{6,4,3},{𝕓𝕒->𝕒5𝕓},{},{13,18},{15,19}},
{"g7230",{10,(Subscript[4, 6]),(Subscript[6, 3]),(Subscript[10, 2]),4},0,"co[ca[12,7],ca[6],2]",{6,2,2,3},{𝕓𝕒->𝕒5𝕓𝕔},{14,32},{3,5,8},{2,19}},

{"C3iQ24",{2,(Subscript[2, 16]),38,4},0,"co[C3,ca[24,11],2]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕2,𝕖𝕒->𝕒𝕖2},{11,13,15},{},{}},
{"E18C4",{20,(Subscript[2, 16]),20,4},0,"co[co[C3,ca[6,5],2],C4]",{2,3,3,4},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2},{3,11,15},{},{}},{"C12iD3",{38,(Subscript[2, 17]),4},0,"co[ca[12],ca[6,5],2]",{3,12,2},{𝕔𝕓->𝕓11𝕔,𝕔𝕒->𝕒2𝕔},{3,5,11},{2,8,15,32},{}},
{"C6nQ12",{4,(Subscript[4, 8]),36,4},0,"co[ca[6],ca[12,5],2]",{3,4,3,2},{𝕓𝕒->𝕒2𝕓,𝕔𝕓->𝕓𝕔2},{10,13,19},{1,8,18,32,36},{}},{"g7235",{22,(Subscript[4, 8]),18,4},0,"co[ca[12,7],ca[6,5],2]",{2,2,2,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕2,𝕖𝕒->𝕒𝕖2},{3,11,20},{},{}},{"g7236",{4.,(Subscript[4, 17]),4},0,"co[C4,C3,C3,C2,0]",{4,3,3,2},{},{10,12,19},{8,15,17},{8,12,19}},
{"D8C3C3",{6,(Subscript[2, 9]),(Subscript[6, 8]),4},0,"co[C3,ca[24,7]]",{4,2,3,3},{𝕓𝕒->𝕒3𝕓},{},{},{}},
{"Q8C3C3",{2,(Subscript[2, 8]),(Subscript[6, 9]),4},0,"co[ca[24,19],C3]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g7239",{10,(Subscript[1, 8]),(Subscript[2, 27]),4},0,"ca[]",{2,2,2,3,3},{𝕒2->𝕓,𝕓2->𝕔,𝕕𝕒->𝕒𝕖,𝕕𝕓->𝕓𝕕𝕖2,𝕕𝕔->𝕔𝕕2,𝕖𝕒->𝕒𝕕𝕖2,𝕖𝕓->𝕓𝕕2𝕖2,𝕖𝕔->𝕔𝕖2},{},{},{}},{"P72",{22,(Subscript[2, 9]),(Subscript[4, 8]),4},0,"ca[]",{2,2,2,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕2,𝕕𝕓->𝕓𝕖,𝕕𝕔->𝕔𝕕2,𝕖𝕓->𝕓𝕕,𝕖𝕔->𝕔𝕖2},{},{},{2,7,8},{{3,1,2,6,5,4},{4,5,6,1,3,2}}},

{"g7241",{10,(Subscript[1, 8]),(Subscript[6, 9]),4},0,"ca[]",{2,2,2,3,3},{𝕒2->𝕔,𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕𝕖2,𝕕𝕓->𝕓𝕖,𝕕𝕔->𝕔𝕕2,𝕖𝕒->𝕒𝕕2𝕖2,𝕖𝕓->𝕓𝕕2,𝕖𝕔->𝕔𝕖2},{},{},{}},{"S4C3",{10,(Subscript[1, 24]),(Subscript[2, 9]),(Subscript[10, 2]),13},0,"co[sgroup[4],C3]",{3,2,2,2,3},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓,𝕕𝕒->𝕒2𝕕,𝕕𝕓->𝕔𝕕,𝕕𝕔->𝕓𝕕},{},{9,13},{3,10}},
{"g7243",{22,(Subscript[1, 24]),(Subscript[4, 2]),(Subscript[6, 3]),13},0,"ca[]",{2,3,3,2,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2,𝕕𝕒->𝕒𝕖,𝕕𝕓->𝕓𝕖,𝕖𝕒->𝕒𝕕,𝕖𝕓->𝕓𝕕𝕖},{},{},{}},
{"A4S3",{16,(Subscript[1, 16]),(Subscript[4, 10]),13},0,"co[Transpose[A4],ca[6,5]]",{3,2,2,3,2},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓,𝕖𝕕->𝕕2𝕖},{},{},{}},{"g7245",{20,(Subscript[2, 8]),(Subscript[4, 9]),4},0,"ca[]",{4,3,3,2},{𝕓𝕒->𝕒𝕔2,𝕔𝕒->𝕒𝕓},{},{},{-8,13}},
{"S3^2C2",{32,(Subscript[2, 4]),(Subscript[8, 4]),4},0,"co[co[ca[6,5],ca[6,5]],C2]",{3,2,3,2,2},{𝕓𝕒->𝕒2𝕓,𝕕𝕔->𝕔2𝕕},{},{},{}},{"A4C6?",{8,(Subscript[2, 24]),(Subscript[8, 2]),13},0,"co[Transpose[A4],ca[6]]",{3,2,2,3,2},{𝕔𝕒->𝕒𝕓,𝕓𝕒->𝕒𝕓𝕔},{},{},{}},{"g7248",{16,(Subscript[4, 6]),(Subscript[16, 2]),4},0,"co[ca[6],ca[12,7],2]",{6,2,3,2},{𝕓𝕒->𝕒5𝕓},{},{2,18,22},{5,7,19}},
{"E18K",{40,(Subscript[4, 8]),4},0,"co[co[C3,ca[6,5],2],C2C2]",{2,3,3,2,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕔2},{-4,5,19},{2,3,18,32},{}},{"C3^2C2^3",{8.,(Subscript[8, 8]),4},0,"co[C3,co[C3,co[C2,co[C2,C2]]]]",{3,3,2,2,2},{},{1,19,20},{3,18,22},{1,-8,19}}};

loop[[73]]={{"C73",{1.,(Subscript[1, 72])},0,"ca[73]",{},{},{},{},{}}};loop[[74]]={{"D74",{38,(Subscript[1, 36])},0,"ca[74,73]",{},{},{},{},{}}};
{"C74",{2.,(Subscript[2, 36])},0,"ca[74]",{},{},{},{},{}};
loop[[75]]={{"C75?",{1.,(Subscript[1, 74])},4,"ca[75]",{75},{},{},{},{}},
{"C5C5iC3",{1,(Subscript[1, 74])},4,"ca[]",{3,5,5},{𝕓𝕒->𝕒𝕓𝕔2,𝕔𝕒->𝕒𝕓𝕔3},{},{},{}},
{"C15C5?",{1.,(Subscript[1, 74])},4,"co[ca[15],ca[5]]",{15,5},{},{},{},{}}};loop[[76]]={{"C19iC4?",{2,(Subscript[2, 18]),38},0,"co[ca[19],C4,2]",{},{},{},{},{}},
{"C19iK?",{40,(Subscript[2, 18])},0,"co[ca[19],C2C2,2]",{},{},{},{},{}},
{"Q76?",{2,(Subscript[2, 18]),38},0,"ca[76,37]",{},{},{},{},{}},{"D76?",{40,(Subscript[2, 18])},0,"ca[76,75]",{},{},{},{},{}},{"C76?",{2.,(Subscript[2, 37])},0,"ca[76]",{},{},{},{},{}},{"C38C2",{4.,(Subscript[4, 18])},0,"co[ca[38],C2]",{},{},{},{},{}},
{"D38C2?",{40,(Subscript[2, 18])},0,"co[ca[38,37],C2]",{},{},{},{},{}},
{"C19C4?",{2.,(Subscript[2, 37])},0,"co[ca[19],C4]",{},{},{},{},{}},
{"C19K?",{4.,(Subscript[4, 18])},0,"co[ca[19],C2C2]",{},{},{},{},{}}};loop[[77]]={{"C77",{1.,(Subscript[1, 76])},0,"ca[77]",{},{},{},{},{}}};loop[[78]]={{"C13iC6?",{14,(Subscript[1, 36]),(Subscript[14, 2])},0,"ca[]",{2,3,13},{𝕔𝕒->𝕒𝕔12},{},{},{}},
{"C13iC2C3?",{2,(Subscript[2, 38])},0,"ca[]",{2,3,13},{𝕔b->"b𝕔3"},{},{},{}},
{"C13S3",{4,(Subscript[1, 26]),(Subscript[4, 12])},0,"co[ca[13],S3]",{2,13,3},{𝕔𝕒->𝕒𝕔2},{},{},{}},
{"C3D26?",{14,(Subscript[1, 36]),(Subscript[14, 2])},0,"co[C3,ca[26,25]]",{2,3,13},{𝕔𝕒->𝕒𝕔12},{},{},{}},
{"D78",{40,(Subscript[1, 38])},0,"ca[78,77]",{39,2},{𝕓𝕒->𝕒38𝕓},{},{},{}},
{"C78?",{2.,(Subscript[2, 38])},0,"ca[78]",{78},{},{},{},{}}};
loop[[79]]={{"C79",{1.,(Subscript[1, 78])},0,"ca[79]",{},{},{},{},{}}};loop[[80]]=(*52 missing groups*){{"C5iC16",{2,(Subscript[2, 19]),(Subscript[10, 4])},0,"ca[]",{2,2,2,2,5},{𝕒2->𝕓,𝕓2->𝕔,𝕔2->𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"C80",{2.,(Subscript[2, 39])},0,"ca[80]",{16,5},{},{},{},{}},{"C5pC16",{2,(Subscript[2, 29]),(Subscript[10, 2])},0,"ca[]",{2,2,2,2,5},{𝕒2->𝕓,𝕓2->𝕔,𝕔2->𝕕,𝕖𝕒->𝕒𝕖2,𝕖𝕓->𝕓𝕖4},{},{},{}},
{"C8D5?",{12,(Subscript[2, 16]),(Subscript[12, 3])},0,"co[ca[8],ca[10,9]]",{2,2,2,2,5},{𝕓2->𝕔,𝕔2->𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"g8005?",{12,(Subscript[2, 16]),(Subscript[12, 3])},0,"ca[]",{2,2,2,2,5},{𝕓2->𝕔,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"g8006",{22,(Subscript[2, 18]),22},0,"ca[]",{2,2,2,2,5},{𝕓2->𝕔,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"D80",{42,(Subscript[2, 19])},0,"ca[80,79]",{2,2,2,2,5},{𝕓2->𝕔𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"C5iQ8",{2,(Subscript[2, 18]),42},0,"co[ca[5],ca[16,7],2]",{2,2,2,2,5},{𝕒2->𝕕,𝕓2->𝕔𝕕,𝕔2->𝕕,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕖𝕒->𝕒𝕖4},{},{},{}},
{"OctC5",{2,(Subscript[2, 4]),(Subscript[14, 5])},0,"co[Oct,C5]",{},{},{},{},{}},{"OctC5n",{10,70},0,"co[Oct,C5n]",{},{},{},{},{}},{"OctiC5n",{2,(Subscript[2, 6]),(Subscript[4, 6]),(Subscript[14, 3])},0,"co[Oct,C5,2]",{},{},{},{},{}}};
loop[[81]]={{"C81",{{1.,3,(Subscript[3, 26])}},0,"ca[81]",{81},{},{},{},{}},{"C9C9?",{1.,9,(Subscript[9, 8])},0,"co[ca[9],ca[9]]",{9,9},{},{},{},{}},
{"C9iC3C3?",{1,27,(Subscript[27, 2])},0,"ca[]",{9,3,3},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"C9iC9?",{{1,9,(Subscript[9, 8])}},0,"ca[]",{9,9},{𝕓𝕒->𝕒4𝕓},{},{},{}},
{"C27C3?",{1.,9,(Subscript[9, 8])},0,"co[ca[27],C3]",{27,3},{},{},{},{}},
{"C27iC3?",{1,9,(Subscript[9, 8])},0,"ca[]",{27,3},{𝕓𝕒->𝕒19𝕓},{},{},{}},
{"C3iC9ic3",{1,45,(Subscript[18, 2])},0,"ca[]",{3,3,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕},{},{},{}},
{"g8108?",{1,27,(Subscript[27, 2])},0,"ca[]",{9,3,3},{𝕓𝕒->𝕒𝕓𝕔},{},{},{}},
{"g8109",{1,63,(Subscript[9, 2])},0,"ca[]",{3,3,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕔𝕓->𝕓𝕔𝕕},{},{},{}},{"g8110?",{1,27,(Subscript[27, 2])},0,"ca[]",{9,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓3𝕔},{},{},{}},

{"g8111",{1.,27,(Subscript[27, 2])},0,"co[co[ca[9],C3],C3]",{9,3,3},{},{},{},{}},
{"C3iC3C3C3?",{1,81},0,"ca[]",{3,3,3,3},{𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕓3𝕔},{},{},{}},
{"g8113?",{1,81},0,"ca[]",{3,3,3,3},{𝕔𝕒->𝕒𝕓2𝕔},{},{},{}},
{"g8114?",{1,27,(Subscript[27, 2])},0,"ca[]",{3,3,9},{𝕓𝕒->𝕒𝕓𝕔6},{},{},{}},
{"C3^4",{1.,81},0,"co[co[co[C3,C3],C3],C3]",{3,3,3,3},{},{},{},{}}};
loop[[96]]={{"C3iC32?",{2,(Subscript[2, 23]),(Subscript[6, 8])},0,"co[C3,ca[32],2]",{2,2,2,2,2,3},{𝕒2->𝕓,𝕓2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"C96",{2.`,(Subscript[2, 47])},0,"ca[96]",{96},{},{},{},{}},{"C4C2iC3?",{8,(Subscript[2, 16]),(Subscript[8, 7])},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"C16S3?",{8,(Subscript[2, 16]),(Subscript[8, 7])},0,"co[ca[16],S3]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"C48C2?",{8,(Subscript[2, 16]),(Subscript[8, 7])},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"D96",{50,(Subscript[2, 23])},0,"ca[96,95]",{2,2,2,2,2,3},{𝕓2->𝕔𝕕,𝕔2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9607",{26,(Subscript[2, 22]),26},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔𝕕,𝕔2->𝕕,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"C3iQ32",{2,(Subscript[2, 22]),50},0,"co[C3,ca[32,15],2]",{2,2,2,2,2,3},{𝕒2->𝕖,𝕓2->𝕔𝕕,𝕔2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"C4C3iC8?",{4,(Subscript[4, 11]),(Subscript[12, 4])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕔2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9610?",{2,(Subscript[2, 23]),(Subscript[6, 8])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"C12iC8?",{4,(Subscript[4, 11]),(Subscript[24, 2])},0,"co[ca[12],C8,2]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9612?",{16,(Subscript[4, 10]),(Subscript[12, 2]),16},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9613",{20,(Subscript[4, 6]),(Subscript[8, 2]),(Subscript[12, 3])},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g9614",{4,(Subscript[4, 5]),(Subscript[8, 2]),(Subscript[12, 2]),32},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g9615",{4,(Subscript[4, 5]),(Subscript[8, 3]),(Subscript[12, 2]),24},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9616",{28,(Subscript[4, 5]),(Subscript[8, 3]),(Subscript[12, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9617",{4,(Subscript[4, 4]),(Subscript[8, 3]),(Subscript[12, 2]),28},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕖,𝕓2->𝕔,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9618?",{4,(Subscript[4, 11]),(Subscript[12, 4])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9619?",{4,(Subscript[4, 11]),(Subscript[12, 4])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕔2->𝕕,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9620?",{4,(Subscript[4, 11]),(Subscript[12, 4])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕕2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9621?",{4,(Subscript[4, 9]),(Subscript[12, 2]),(Subscript[16, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9622?",{4,(Subscript[4, 11]),(Subscript[12, 4])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9623",{4,(Subscript[4, 10]),24,28},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g9624?",{4,(Subscript[4, 11]),(Subscript[24, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"C24pC4",(*25*){4,(Subscript[4, 11]),48},0,"co[ca[24],C4,2]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9626?",{4,(Subscript[4, 11]),(Subscript[24, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕔,𝕓2->𝕕,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9627?",{16,(Subscript[4, 10]),(Subscript[12, 2]),16},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9628",{28,(Subscript[4, 11]),24},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔𝕕,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕔,𝕔𝕒->𝕒𝕔𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g9629?",{4,(Subscript[4, 9]),(Subscript[12, 2]),(Subscript[16, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕕,𝕓2->𝕔,𝕔2->𝕖,𝕕2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g9630",{28,(Subscript[4, 11]),(Subscript[12, 2])},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕔,𝕔2->𝕖,𝕓𝕒->𝕒𝕓𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2,"𝕕𝕓"->"𝕓𝕕𝕖"},{},{},{}},
{"g9670",{20,(Subscript[2, 32]),(Subscript[4, 3])},0,"ca[]",{2,3,2,2,2,2},{"𝕔𝕒"->"𝕒𝕔𝕖","𝕕𝕒"->"𝕒𝕕𝕗","𝕔𝕓"->"𝕓𝕕","𝕕𝕓"->"𝕓𝕔𝕕","𝕖𝕓"->"𝕓𝕗","𝕗𝕓"->"𝕓𝕖𝕗"},{},{},{}},{"g9699",{16,(Subscript[4, 4]),(Subscript[8, 3]),16,24},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕖,𝕔2->𝕕,𝕔𝕒->𝕒𝕔𝕖,𝕗𝕒->𝕒𝕗2,𝕔𝕓->𝕓𝕔𝕖},{},{},{}},
{"Q16S3",(*124*){8,(Subscript[2, 6]),(Subscript[8, 2]),(Subscript[10, 2]),40},0,"co[ca[16,7],S3]",{},{},{},{},{}},
{"C12D8",(*165*){12,(Subscript[4, 6]),(Subscript[12, 5])},0,"co[ca[12],ca[8,7]]",{},{},{},{},{}},
{"C12Q8",(*166*){4,(Subscript[4, 5]),(Subscript[12, 6])},0,"co[ca[12],ca[8,3]]",{},{},{},{},{}},{"C6D16",(*179*){20,(Subscript[4, 9]),(Subscript[20, 2])},0,"co[ca[6],ca[16,15]]",{2,2,2,3,2,2},{"𝕖2"->"𝕗","𝕓𝕒"->"𝕒𝕓𝕖","𝕖𝕒"->"𝕒𝕖𝕗","𝕖𝕓"->"𝕓𝕖𝕗"},{},{},{}},
{"C6Q16",(*181*){4,(Subscript[4, 8]),(Subscript[20, 3])},0,"co[ca[6],ca[16,7]]",{},{},{},{},{}},{"A4Q8",(*185*){8,(Subscript[2, 8]),(Subscript[6, 8]),24},0,"co[A4,Q8]",{},{},{},{},{}},
{"C4S4",(*186*){20,(Subscript[2, 16]),(Subscript[4, 6]),20},0,"co[C4,sgroup[4]]",{},{},{},{},{}},{"KA4iC2?",(*195*){16,(Subscript[4, 16]),16},0,"co[C2C2,A4,C2,1,2]",{2,2,3,2,2,2},{𝕓2->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕕2,𝕖𝕒->𝕒𝕗,𝕗𝕒->𝕒𝕖,𝕖𝕕->𝕕𝕗,𝕗𝕕->𝕕𝕖𝕗},{},{},{}},{"C2C4A4?",(*196*){16,(Subscript[4, 16]),16},0,"co[C2,C4,A4,1]",{2,2,3,2,2,2},{𝕓2->𝕕,𝕖𝕔->𝕔𝕗,𝕗𝕔->𝕔𝕖𝕗},{},{},{}},{"D8A4",(*197*){24,(Subscript[2, 8]),(Subscript[6, 8]),8},0,"co[ca[8,7],A4]",{4,2,3,2,2},{𝕓𝕒->𝕒3𝕓,𝕕𝕔->𝕔𝕕𝕖,𝕖𝕔->𝕔𝕕},{},{},{}},
{"KSL23?",(*198*){8,(Subscript[8, 8]),24},0,"co[C2C2,SL23]",{2,2,3,2,2,2},{𝕕2->𝕗,𝕖2->𝕗,𝕕𝕔->𝕔𝕖,𝕖𝕔->𝕔𝕕𝕖,𝕖𝕕->𝕕𝕖𝕗},{},{},{}},{"Q8A4?",(*199*){8,(Subscript[2, 8]),(Subscript[6, 8]),24},0,"co[ca[8,3],A4]",{2,2,3,2,2,2},{𝕒2->𝕕,𝕓2->𝕕,𝕓𝕒->𝕒𝕓𝕕,𝕖𝕔->𝕔𝕗,𝕗𝕔->𝕔𝕖𝕗},{},{},{}},
{"C2SL23iC2?",(*200*){16,(Subscript[4, 16]),16},0,"co[C2,co[SL23,C2,2]]",{2,2,3,2,2,2},{𝕓2->𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕕𝕔->𝕔𝕖,𝕖𝕔->𝕔𝕕𝕖,𝕖𝕕->𝕕𝕖𝕗},{},{},{}},
{"g96202",{16,(Subscript[4, 6]),(Subscript[8, 2]),(Subscript[12, 2]),16},0,"ca[]",{2,2,3,2,2,2},{𝕓2->𝕗,𝕕2->𝕗,𝕖2->𝕗,𝕕𝕔->𝕔𝕖,𝕖𝕔->𝕕𝕖,𝕖𝕕->𝕕𝕖𝕗},{},{},{}},
{"g96203?",{20,(Subscript[2, 32]),12},0,"ca[]",{3,2,2,2,2,2},{𝕕2->𝕗,𝕖2->𝕗,𝕓𝕒->𝕒𝕔,𝕔𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕖,𝕖𝕒->𝕒𝕕𝕖,𝕖𝕕->𝕕𝕖𝕗},{},{},{}},{"g96204?",{20,(Subscript[2, 32]),12},0,"ca[]",{3,2,2,2,2,2},{𝕓𝕒->𝕒𝕔,𝕔𝕒->𝕒𝕓𝕔,𝕕𝕒->𝕒𝕖,𝕕𝕔->𝕔𝕕𝕗,𝕖𝕒->𝕒𝕕𝕖,𝕖𝕓->𝕓𝕖𝕗},{},{},{}},{"g96205",{8,(Subscript[8, 4]),56},0,"ca[]",{2,2,2,2,2,3},{𝕒2->𝕖,𝕕2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96206?",{32,(Subscript[8, 4]),32},0,"ca[]",{2,2,2,2,2,3},{𝕕2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"KD12",(*207*){56,(Subscript[8, 5])},0,"co[C2C2,ca[24,23]]",{2,2,2,2,2,3},{𝕕2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96208?",{32,(Subscript[8, 4]),32},0,"ca[]",{2,2,2,2,2,3},{𝕔2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96209",{48,(Subscript[4, 2]),(Subscript[12, 2]),16},0,"ca[]",{2,2,2,2,2,3},{𝕕𝕔->𝕔𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96210?",{24,(Subscript[4, 2]),(Subscript[12, 2]),40},0,"ca[]",{2,2,2,2,2,3},{𝕔2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕔->𝕔𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96211",{36,(Subscript[4, 2]),(Subscript[12, 2]),28},0,"ca[]",{2,2,2,2,2,3},{𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96212",{16,(Subscript[4, 2]),(Subscript[12, 2]),48},0,"ca[]",{2,2,2,2,2,3},{𝕔2->𝕖,𝕕2->𝕖,𝕕𝕔->𝕔𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96213?",{28,(Subscript[4, 2]),(Subscript[12, 2]),36},0,"ca[]",{2,2,2,2,2,3},{𝕔2->𝕖,𝕕2->𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕕𝕔->𝕔𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96214?",{28,(Subscript[4, 2]),(Subscript[12, 2]),36},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕖,𝕔2->𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96215?",{32,(Subscript[8, 4]),32},0,"ca[]",{2,2,2,2,2,3},{𝕔2->𝕖,𝕕𝕓->𝕓𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96216",{44,(Subscript[8, 4]),20},0,"ca[]",{2,2,2,2,2,3},{𝕕2->𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},{"g96217",{20,(Subscript[8, 4]),44},0,"ca[]",{2,2,2,2,2,3},{𝕓2->𝕖,𝕔2->𝕖,𝕕2->𝕖,𝕔𝕓->𝕓𝕔𝕖,𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96218",{16,(Subscript[16, 2]),48},0,"co[ca[6],C4,C2,C2,1,1,2]",{2,2,2,2,2,3},{𝕒2->𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96219",{40,(Subscript[16, 2]),24},0,"co[ca[6],C4,C2,C2,1,2,2]",{2,2,2,2,2,3},{𝕕𝕒->𝕒𝕕𝕖,𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96220",{16.,(Subscript[16, 5])},0,"co[ca[6],co[C4,C2,C2,2]]",{2,2,2,2,3,2},{𝕒2->𝕗},{},{},{}},{"g96221",{24,(Subscript[8, 3]),(Subscript[24, 2])},0,"co[ca[6],C4,C2,C2,1,2]",{2,2,2,2,3,2},{𝕓𝕒->𝕒𝕓𝕗},{},{},{}},{"g96222",{8,(Subscript[8, 2]),(Subscript[24, 3])},0,"co[cLoop[0,3,-5],C2,C2,1]",{2,2,2,2,3,2},{𝕒2->𝕗,𝕓2->𝕗,𝕓𝕒->𝕒𝕓𝕗},{},{},{}},{"g96223",{16,(Subscript[16, 5])},0,"co[cLoop[3,0,-5],C2,C2,1]",{2,2,2,2,3,2},{𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕗},{},{},{}},
{"g96224",{20,(Subscript[12, 3]),(Subscript[20, 2])},0,"co[cLoop[3,1,-5],C2]",{2,2,2,2,3,2},{𝕓𝕒->𝕒𝕓𝕗,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g96225",{12,(Subscript[12, 2]),(Subscript[20, 3])},0,"co[cLoop[4,0,-5],C2]",{2,2,2,2,3,2},{𝕓2->𝕗,𝕔2->𝕗,𝕓𝕒->𝕒𝕓𝕗,𝕔𝕓->𝕓𝕔𝕗,𝕕𝕒->𝕒𝕕𝕗},{},{},{}},
{"g96226",{40,(Subscript[4, 8]),(Subscript[8, 3])},0,"ca[]",{2,2,2,3,2,2},{𝕕𝕒->𝕒𝕕2,𝕖𝕒->𝕒𝕗,𝕖𝕕->𝕕𝕗,𝕗𝕒->𝕒𝕖,𝕗𝕕->𝕕𝕖𝕗},{},{},{}},
{"g96227",{28,(Subscript[1, 32]),(Subscript[4, 9])},0,"ca[]",{2,3,2,2,2,2},{𝕓𝕒->𝕒𝕓2,𝕔𝕒->𝕒𝕕,𝕔𝕓->𝕓𝕕,𝕕𝕒->𝕒𝕔,𝕕𝕓->𝕓𝕔𝕕,𝕖𝕒->𝕒𝕗,𝕖𝕓->𝕓𝕖𝕗,𝕗𝕒->𝕒𝕖,𝕗𝕓->𝕓𝕖},{},{},{}},{"g96228",{32,(Subscript[8, 8])},0,"co[A4,C2C2,C2,1]",{2,2,2,3,2,2},{𝕖𝕕->𝕕𝕗,𝕗𝕕->𝕕𝕖𝕗},{},{},{}},
{"g96229",{32,(Subscript[2, 32])},0,"ca[]",{2,3,2,2,2,2},{𝕔𝕓->𝕓𝕕,𝕕𝕓->𝕓𝕔𝕕,𝕖𝕓->𝕓𝕗,𝕗𝕓->𝕓𝕖𝕗},{},{},{}},{"g96230",{64,(Subscript[16, 2])},0,"co[S3,C2C2,C2C2,1]",{2,2,2,2,2,3},{𝕗𝕒->𝕒𝕗2},{},{},{}},
{"g96231",{32.`,(Subscript[32, 2])},0,"co[ca[6],C2C2,C2C2,1]",{2,2,2,2,2,3},{},{},{},{}},
{"g96?",{20,(Subscript[8, 4]),(Subscript[12, 2]),20},0,"co[C4,ca[12,7],C2,2]",{},{},{},{},{}},
{"g96??",{28,(Subscript[4, 10]),28},0,"co[C4,ca[12,1],C2,2]",{},{},{},{},{}}};
loop[[104]]={{"g104003",{2,(Subscript[2, 38]),26},0,"ca[]",{13,8},{𝕓𝕒->𝕒5𝕓},{},{},{}}};
loop[[120]]={{"S5",(*g12034*){26,(Subscript[1, 24]),(Subscript[2, 35])},0,"sgroup[5]",{},{},{},{},{},"{{{1,2,3,4}},{{1,5,4,3,2}}}"},{"SL25",{2,(Subscript[2, 44]),30},0,"pe[{{1,3,5,7,9,6,12,14,15,17,19,8,11,4,2,13,23,18,22,24,21,16,20,10},
{2,4,6,8,10,11,13,3,16,18,20,21,22,23,5,9,19,7,1,17,24,12,14,15}},120]",{},{},{},{},{},"{{{1,2,4,8},{3,6,9,5},{7,12,13,17},{10,14,11,15},{16,20,21,24},{18,22,19,23}},{{1,3,7},{2,5,10},{4,9,13},{6,11,8},{12,16,20},{14,18,22},{15,19,23},{17,21,24}}}"}};loop[[128]]={{"CL70",{-64,64,64,8064},0,"cLoop[7.]",{},{},{},{},{}}};loop[[168]]={{"SL32",{22,(Subscript[1, 104]),(Subscript[2, 21])},0,"pe[{{2,4,5,1,7,6,3},{1,3,2,6,5,4,7}},170]",{},{},{},{},{},{{{2,3},{4,6}},{{1,2,4},{3,5,7}}}}};
loop[[169]]={{"Unrecognised",{},0,"Unrecognised",{},{},{},{},{}}};

9.6 Deleted.

9.7 Shapes, Polar-Vector, Hyperbolics, sh, toPol, toVec, tohyPol, tohyVec for 2, 3, & 4 element loops.

sd["C2"]:=(el={ø,𝕒};rofu={};gi={1,2,1,1};gp={1,1};sh={{{ø-𝕒}},{{ø+𝕒}}});
toPol[{x_,y_},"C2"]:={x-y,x+y}
toVec[{x_,y_},"C2"]:={x+y,y-x}/2
tohyPol[{a_,b_},"C2"]:=Chop[{(a^2)-(b^2),arcTanh[a,b]}]
tohyVec[{uu_,ϕ_},"C2"]:=Chop[(Sqrt[uu]) {Cosh[ϕ],Sinh[ϕ]}]

sd["C4c"]:=(el={ø,𝕒};rofu={};gi={1,-2,1};gp={1,0.};sh={{{(ø^2)+(𝕒^2)}}});
toPol[{a_,b_},"C4c"]:={(ø^2)+(𝕒^2),ArcTan[ø,𝕒]}
toVec[{x_,y_},"C4c"]:={(Sqrt[x]) Cos[y],(Sqrt[x]) Sin[y]};
sd["CL10"]:=(el={ø,𝕒};rofu={};gi={1,2,1,1};sh={{{ø-𝕒,ø+𝕒}}});sd["CL01"]:=(el={ø,𝕒};rofu={};gi={1,-2,1};sh={{{(ø^2)+(𝕒^2)}}});

sd["C3"]:=(el={ø,𝕒,𝕒2};rofu={};gi={1,3,2,1,1};gp={1,1,0.};sh={{{ø+𝕒+𝕒2}},{{((ø-𝕒)^2+(𝕒-𝕒2)^2+(𝕒2-ø)^2)/2}}});
toPol[{ø_,𝕒_,𝕒2_},"C3"]:={ø+𝕒+𝕒2,((ø-𝕒)^2+(𝕒-𝕒2)^2+(𝕒2-ø)^2)/2,
ArcTan[2*ø-𝕒-𝕒2,-Sqrt[3]*(𝕒-𝕒2)]}
toVec[{α_,rr_,θ_},"C3"]:=Chop[{α+2*Sqrt[rr]*Cos[θ],α+2*Sqrt[rr]*Cos[θ+2*Pi/3],
α+2*Sqrt[rr]*Cos[θ-2*Pi/3]}/3]

sd["C3C2c"]:=(el={ø,𝕒,𝕒2};rofu={};gi={1,-3,-2,1,1};gp={1,1,0.};sh={{{ø-𝕒+𝕒2}},{{((((ø+𝕒))^2)+(((-ø+𝕒2))^2)+(((𝕒+𝕒2))^2))/2}}});toPol[{a_,b_,c_},"C3C2c"]:={a-b+c,((a+b)^2+(b+c)^2+(c-a)^2)/2,
ArcTan[2*a+b-c,-Sqrt[3]*(b+c)]};
toVec[{α_,rr_,θ_},"C3C2c"]:=Chop[{α+2*Sqrt[rr]*Cos[θ],-α-2*Sqrt[rr]*Cos[θ-2*Pi/3],
α+2*Sqrt[rr]*Cos[θ+2*Pi/3]}/3];
sd["C12c"]:=(el={ø,𝕒,𝕒2};rofu={};gi={1,3 I,2 I,1,1};gp={1,1,0.};sh={{{ø+I 𝕒-𝕒2}},{{(1/2) ((((ø-I 𝕒))^2)+(((ø+𝕒2))^2)+(((I 𝕒+𝕒2))^2))}}});
toPol[{a_,b_,c_},"C12c"]:={a+I b-c, ((((a-I b))^2)+(((a+c))^2)+(((I b+c))^2))/2,
ArcTan[2*a-I b+c,Sqrt[3]*(I b+c)]}
toVec[{α_,rr_,θ_},"C12c"]:=Chop[{α+2*Sqrt[rr]*Cos[θ],
-I(α+2*Sqrt[rr]*Cos[θ-2*Pi/3]),-(α+2*Sqrt[rr]*Cos[θ+2*Pi/3])}/3];
sd["C4C3c"]:=(el={ø,𝕒,𝕒2};rofu={};gi={1,-3,-2,1,1};gp=={1,1,0.};sh={{{ø+I 𝕒+I 𝕒2}},{{(1/2) ((((ø-I 𝕒))^2)-(((𝕒-𝕒2))^2)+(((ø-I 𝕒2))^2))}}});
toPol[{a_,b_,c_},"C4C3c"]:={a-I b-c, ((((a+I b))^2)+(((I b-c))^2)+(((c+a))^2))/2,
ArcTan[2*a+I b+c,Sqrt[3]*(-I b+c)]}
toVec[{α_,rr_,θ_},"C4C3c"]:=Chop[{α+2*Sqrt[rr]*Cos[θ],I(α+2*Sqrt[rr]*Cos[θ-2*Pi/3]),-(α+2*Sqrt[rr]*Cos[θ+2*Pi/3])}/3]

sd["C4"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,4,3,2,1,1,1};gp={1,1,1,0.};sh={{{ø+𝕒+𝕒2+𝕒3}},{{ø-𝕒+𝕒2-𝕒3}},{{(((ø-𝕒2))^2)+(((𝕒-𝕒3))^2)}}});
toPol[{a_,b_,c_,d_},"C4"]:={a+b+c+d,a-b+c-d,(((a-c))^2)+(((b-d))^2),
ArcTan[a-c,b-d]}
toVec[{α_,β_,ϵϵ_,σ_},"C4"]:={α+β+2*Sqrt[ϵϵ]*Cos[σ],α-β+2*Sqrt[ϵϵ]*Sin[σ],α+β-2*Sqrt[ϵϵ]*Cos[σ],
α-β-2*Sqrt[ϵϵ]*Sin[σ]}/4
tohyPol[{a_,b_,c_,d_},"C4"]:=Chop[{(a+c)^2-(b+d)^2,arcTanh[a+c,b+d],(a-c)^2+(b-d)^2,ArcTan[a-c,b-d]}]
tohyVec[{uu_,ϕ_,rr_,θ_},"C4"]:=Module[{r=Sqrt[rr],u=Sqrt[uu]},Chop[r*{Cos[θ],Sin[θ],-Cos[θ],-Sin[θ]}/2+u*{Cosh[ϕ],Sinh[ϕ],Cosh[ϕ],Sinh[ϕ]}/2]]

sd["C2C2"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,2,3,4,1,1,1,1};gp={1,1,1,1};sh=
{{{ø+𝕒-𝕓-𝕒𝕓}},{{ø-𝕒+𝕓-𝕒𝕓}},{{ø-𝕒-𝕓+𝕒𝕓}},{{ø+𝕒+𝕓+𝕒𝕓}}});
toPol[{a_,b_,c_,d_},"C2C2"]:={a+b-c-d,a-b+c-d,a-b-c+d,a+b+c+d};
toVec[{o1_,o2_,o3_,o4_},"C2C2"]:={o1+o2+o3+o4,o1-o2-o3+o4,-o1+o2-o3+o4,-o1-o2+o3+o4}/4
tohyPol[{a_,b_,c_,d_},"C2C2"]:=Chop[{(a+c)^2-(b+d)^2,arcTanh[a+c,b+d],
(a-c)^2-(b-d)^2,arcTanh[a-c,b-d]}]
tohyVec[{uu_,ϕ_,vv_,ψ_},"C2C2"]:=Module[{v=Sqrt[vv],u=Sqrt[uu]},
Chop[v*{Cosh[ψ],Sinh[ψ],-Cosh[ψ],-Sinh[ψ]}/2+u*{Cosh[ϕ],Sinh[ϕ],Cosh[ϕ],Sinh[ϕ]}/2]]

sd["Qr"]:=(el=Take[el2,4];rofu={};gi={1,-2,-3,-4,2};gp={1,0.,1,0.};sh={{{(ø^2)+(𝕒^2)+((𝕒𝕓)^2)+(𝕓^2)}}});

sd["P4"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,2,3,4,2};gp={1,0.,1,0.};sh={{{(ø^2)-(𝕒^2)-(𝕓^2)-((𝕒𝕓)^2)}}});

sd["Dav"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,-2,-3,4,1,1};gp={1,0.,1,0.};sh={{{(((𝕒+𝕒2))^2)+(((ø-𝕒3))^2)}},{{(((𝕒 -𝕒2))^2)+(((ø+𝕒3))^2)}}});
toPol[{a_,b_,c_,d_},"Dav"]:={(((a-d))^2)+(((b+c))^2),ArcTan[a-d,b+c],
(((a+d))^2)+(((b-c))^2),ArcTan[a+d,b-c]} ;
toVec[{rr_,ρ_,ss_,σ_},"Dav"]:=
{ (Sqrt[rr]) Cos[ρ]+(Sqrt[ss]) Cos[σ], (Sqrt[rr]) Sin[ρ]+(Sqrt[ss]) Sin[σ], (Sqrt[rr]) Sin[ρ]-(Sqrt[ss]) Sin[σ],-(Sqrt[rr]) Cos[ρ]+(Sqrt[ss]) Cos[σ]}/2;

sd["O2"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,-2,3,-4,1,1};gp={1,0.,1,0.};sh=
{{ {(((𝕒-𝕒𝕓))^2)+(((ø-𝕓))^2)}},{{(((𝕒+𝕒𝕓))^2)+(((ø+𝕓))^2)}}});toPol[{a_,b_,c_,d_},"O2"]:= {(((a-c))^2)+(((b-d))^2),ArcTan[a-c,b-d],
(((a+c))^2)+(((b+d))^2),ArcTan[a+c,b+d]} ;toVec[{rr_,ρ_,ss_,σ_},"O2"]:={  (Sqrt[rr]) Cos[ρ]+(Sqrt[ss]) Cos[σ], (Sqrt[rr]) Sin[ρ]+(Sqrt[ss]) Sin[σ],
-(Sqrt[rr]) Cos[ρ]+(Sqrt[ss])Cos[σ], -(Sqrt[rr]) Sin[ρ]+(Sqrt[ss]) Sin[σ]}/2;

sd["C8r"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,4,-3,2,1,1};sh={{{(ø^2)+(𝕒^2)+((𝕒2)^2)+((𝕒3)^2)+(Sqrt[2]) (ø 𝕒-𝕒 𝕒2+ø 𝕒3+𝕒2 𝕒3)}},{{(ø^2)+(𝕒^2)+((𝕒2)^2)+((𝕒3)^2)-(Sqrt[2]) (ø 𝕒-𝕒 𝕒2+ø 𝕒3+𝕒2 𝕒3)}}});
sd["C3C4j"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,-4,3,-2,1,1,1};gp={1,1,1,0.};sh={{{ø+𝕒-𝕒2-𝕒3,ø-𝕒-𝕒2+𝕒3}},{{(((ø+𝕒2))^2)+(((𝕒+𝕒3))^2)}}});
toPol[{a_,b_,c_,d_},"C3C4j"]:={a+b-c-d,a-b-c+d,(((a+c))^2)+(((b+d))^2),ArcTan[a+c,b+d]};
toVec[{α_,β_,ϵϵ_,σ_},"C3C4j"]:={α+β+2*Sqrt[ϵϵ]*Cos[σ],
α-β+2*Sqrt[ϵϵ]*Sin[σ],
-α-β+2*Sqrt[ϵϵ]*Cos[σ],
-α+β+2*Sqrt[ϵϵ]*Sin[σ]}/4;

sd["CL2"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,2,3,-4,2};gp={1,0.,1,0.};
sh={{ {(ø^2)-(𝕒^2)+((𝕒𝕓)^2)-(𝕓^2)}}});
sd["CL20"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,2,3,-4,2};gp={1,0.,1,0.};sh= {{{(ø^2)-(𝕒^2)+((𝕒𝕓)^2)-(𝕓^2)}}});
sd["CL11"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,2,-3,4,2};sh={{{(ø^2)-(𝕒^2)-((𝕒𝕓)^2)+(𝕓^2)}}});
sd["CL02"]:=(el={ø,𝕒,𝕓,𝕒𝕓};rofu={};gi={1,-2,-3,-4,2};sh={{{(ø^2)+(𝕒^2)+((𝕒𝕓)^2)+(𝕓^2)}}});

sd["C4C2r"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,-4,3,-2,1,1,1};gp={1,1,1,0.};sh=
{{{ø+𝕒+𝕒2-𝕒3}},{{ø-𝕒+𝕒2+𝕒3}},{{(((ø-𝕒2))^2)+(((𝕒+𝕒3))^2)}}});
toPol[{a_,b_,c_,d_},"C4C2r"]:= {a+b+c-d,a-b+c+d,(((a-c))^2)+(((b+d))^2),ArcTan[a-c,b+d]} 
toVec[{α_,β_,ϵϵ_,σ_},"C4C2r"]:=
{α+β+2*Sqrt[ϵϵ]*Cos[σ],
α-β+2*Sqrt[ϵϵ]*Sin[σ],
α+β-2*Sqrt[ϵϵ]*Cos[σ],
-α+β+2*Sqrt[ϵϵ]*Sin[σ]}/4
tohyPol[{a_,b_,c_,d_},"C4C2r"]:=Chop[{(a+c)^2-(b-d)^2,arcTanh[a+c,b-d],(a-c)^2+(b+d)^2,ArcTan[a-c,b+d]}]
tohyVec[{uu_,ϕ_,rr_,θ_},"C4C2r"]:=Module[{r=Sqrt[rr],u=Sqrt[uu]},Chop[r*{Cos[θ],Sin[θ],-Cos[θ],Sin[θ]}/2+u*{Cosh[ϕ],Sinh[ϕ],Cosh[ϕ],-Sinh[ϕ]}/2]]
sd["P16c"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,-2,-3,4,2};gp={1,0.,1,0.};sh=
{{{(ø^2)+(𝕒^2)+((𝕒2)^2)-((𝕒3)^2)}}});
sd["Q4n"]:=(el={ø,𝕒,𝕒2,𝕒3};rofu={};gi={1,2,3,4,1,1};gp=.;
sh={{{(ø^2)-(𝕒^2)-((𝕒2)^2)-((𝕒3)^2)}},{{(ø^2)+(𝕒^2)+((𝕒2)^2)+((𝕒3)^2)}}});

9.8 Shapes, Polar-Vector, Hyperbolics, sh, toPol, toVec, tohyPol, tohyVec for 5 & 6 element loops.

sd["C5"]:=(el={ø,𝕒,𝕒2,𝕒3,𝕒4};rofu={};gp=.;gi={1,5,4,3,2,1,1};sh=
{{{ø+𝕒+𝕒2+𝕒3+𝕒4}},{{-5(((ø 𝕒-ø 𝕒2+𝕒 𝕒2-ø 𝕒3-𝕒 𝕒3+𝕒2 𝕒3+ø 𝕒4-𝕒 𝕒4-𝕒2 𝕒4+𝕒3 𝕒4))^2)/4+((((((ø-𝕒))^2)+(((ø-𝕒2))^2)+(((𝕒-𝕒2))^2)+(((𝕒-𝕒3))^2)+(((𝕒2-𝕒3))^2)+(((-ø+𝕒3))^2)+(((𝕒2-𝕒4))^2)+(((𝕒3-𝕒4))^2)+(((-ø+𝕒4))^2)+(((-𝕒+𝕒4))^2)))^2)/16}}});(*{a+b+c+d+e,( (a^2)+ (b^2)+ (c^2)+ (d^2)+ (e^2)-(1+(Sqrt[5]))( a b+b c+c d+a e+d e)/2-(1-(Sqrt[5])) (a c+a d+b d+b e+c e)/2), ( (a^2)+ (b^2)+ (c^2)+ (d^2)+ (e^2)-(1-(Sqrt[5])) ( a b+b c+c d+a e+d e)/2-(1+(Sqrt[5])) (a c+a d+b d+b e+c e)/2)}*)
toVec[{α_,ϵ_,σ_},"C5"]:={α+ϵ*Sin[σ],α+ϵ*Sin[σ+2π/5],
α+ϵ*Sin[σ+4π/5],α+ϵ*Sin[σ+6π/5],α+ϵ*Sin[σ+8π/5]}/5

{a+b+c+d+e,( (a^2)+ (b^2)+ (c^2)+ (d^2)+ (e^2)-(1+(Sqrt[5]))( a b+b c+c d+a e+d e)/2-(1-(Sqrt[5])) (a c+a d+b d+b e+c e)/2), ( (a^2)+ (b^2)+ (c^2)+ (d^2)+ (e^2)-(1-(Sqrt[5])) ( a b+b c+c d+a e+d e)/2-(1+(Sqrt[5])) (a c+a d+b d+b e+c e)/2)}/.{a->ø,b->a,c->b,d->c,e->d};

sd["C6"]:=(el=Take[el3,6];rofu={};gi={1,3,2,4,6,5,1,1,1,1};gp={1,1,1,0.,1,0.};sh=
{{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒𝕓+𝕓}},{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒𝕓-𝕓}}{{((((𝕒-𝕒2-𝕒2𝕓+𝕒𝕓))^2)+(((ø-𝕒2-𝕒2𝕓+𝕓))^2)+(((ø-𝕒-𝕒𝕓+𝕓))^2))/2}}, {{((((𝕒-𝕒2+𝕒2𝕓-𝕒𝕓))^2)+(((ø-𝕒2+𝕒2𝕓-𝕓))^2)+(((ø-𝕒+𝕒𝕓-𝕓))^2))/2}}});
toVec[{α_,δ_,ηη_,χ_,κκ_,ψ_},"C6"]:=Module[{η=2(Sqrt[ηη]),κ=2(Sqrt[κκ])},{  α+δ+η Cos[χ]+κ Cos[ψ],α+δ+η Cos[χ+2 π/3]+κ Cos[ψ+2π/3],α+δ+η Cos[χ-2 π/3]+κ Cos[ψ-2 π/3],
α-δ+η Cos[χ]-κ Cos[ψ],α-δ+η Cos[χ+2 π/3]-κ Cos[ψ+2π/3],α-δ+η Cos[χ-2 π/3]-κ Cos[ψ-2 π/3]}/6]
toPol[{a_,b_,c_,d_,e_,f_},"C6"]:=Module[{a1=Chop[2a-b-c+2d-e-f],a2=Chop[2a-b-c-2d+e+f],b1=Chop[Simplify[c-b-e+f]],b2=Chop[Simplify[c-b+e-f]]},{a+b+c+d+e+f,a+b+c-d-e-f,((((a-b+d-e))^2)+(((b-c+e-f))^2)+(((c-a+f-d))^2))/2,ArcTan[a1,Sqrt[3]b1],((((a-b-d+e))^2)+(((b-c-e+f))^2)+(((c-a-f+d))^2))/2,ArcTan[a2,Sqrt[3]b2]}]
tohyPol[{a_,b_,c_,d_,e_,f_},"C6"]:=Module[{a1=Chop[2a-b-c+2d-e-f],a2=Chop[2a-b-c-2d+e+f],b1=Chop[Simplify[c-b-e+f]],b2=Chop[Simplify[c-b+e-f]]},{(((a+b+c))^2)-(((d+e+f))^2),arcTanh[a+b+c,d+e+f],((((a-b+d-e))^2)+(((b-c+e-f))^2)+(((c-a+f-d))^2))/2,ArcTan[a1,Sqrt[3]b1],((((a-b-d+e))^2)+(((b-c-e+f))^2)+(((c-a-f+d))^2))/2,ArcTan[a2,Sqrt[3]b2]}]
tohyVec[{γγ_,δ_,ηη_,χ_,κκ_,ψ_},"C6"]:=Module[{γ=(Sqrt[γγ]),η=(Sqrt[ηη]),κ=(Sqrt[κκ])},{ γ Cosh[δ]+η Cos[χ]+κ Cos[ψ],γ Cosh[δ]+η Cos[χ+2 π/3]+κ Cos[ψ+2π/3],γ Cosh[δ]+η Cos[χ-2 π/3]+κ Cos[ψ-2 π/3],γ Sinh[δ]+η Cos[χ]-κ Cos[ψ],γ Sinh[δ]+η Cos[χ+2 π/3]-κ Cos[ψ+2π/3],γ Sinh[δ]+η Cos[χ-2 π/3]-κ Cos[ψ-2 π/3]}/3]

sd["S3"]:=(el=Take[el3,6];(*rofu={};*)gi={1,2,5,4,3,6,1,1,2};gp={1,1,1,0.,1,0.};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒𝕓+𝕓}},{{ø-𝕒+𝕒2-𝕒2𝕓+𝕒𝕓-𝕓}},{{.5((((ø-𝕒2))^2)-(((-𝕒+𝕒2𝕓))^2)+(((𝕒2-𝕒𝕓))^2)+(((-ø+𝕒𝕓))^2)-(((𝕒-𝕓))^2)-(((-𝕒2𝕓+𝕓))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_},"S3"]:=Module[{ace=((((a-c))^2)+(((c-e))^2)+(((e-a))^2))/2,χ=ArcTan[2 a-c-e,Sqrt[3](e-c)],bdf=((((b-d))^2)+(((d-f))^2)+(((f-b))^2))/2,ψ=ArcTan[2 b-d-f,Sqrt[3](f-d)]},{a+b+c+d+e+f,a-b+c-d+e-f,ace-bdf,χ,ace,ψ}];
toVec[{γ_,δ_,ηη_,χ_,κκ_,ψ_},"S3"]:=Module[{η=4(Sqrt[κκ]),κ=4(Sqrt[κκ-ηη])},{ γ+δ+η Cos[χ] ,γ-δ+κ  Cos[ψ],γ+δ+η Cos[χ+2 π/3],γ-δ+κ  Cos[ψ+2π/3],γ+δ+η Cos[χ-2 π/3],γ-δ+κ  Cos[ψ-2 π/3]}/6];

shS3={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒𝕓+𝕓}},{{ø-𝕒+𝕒2-𝕒2𝕓+𝕒𝕓-𝕓}},{{.5((((ø-𝕒2))^2)-(((-𝕒+𝕒2𝕓))^2)+(((𝕒2-𝕒𝕓))^2)+(((-ø+𝕒𝕓))^2)-(((𝕒-𝕓))^2)-(((-𝕒2𝕓+𝕓))^2))}}}/.{𝕒2𝕓->aab,𝕒2->aa,𝕒𝕓->ab,𝕒->a,𝕓->b};

sd["C3C4c"]:=
(el=Take[el3,6];rofu={};gp={1,0.,1,0.,1,0.};gi={1,3,2,-4,-6,-5,1,1,1};sh=
{{{(((ø+𝕒+𝕒2))^2)+(((𝕒2𝕓+𝕒𝕓+𝕓))^2)}},{{.75 ((((rs3 (ø+𝕒-2 𝕒2)+𝕒𝕓-𝕓))^2)+(((ø-𝕒+rs3 (-2 𝕒2𝕓+𝕒𝕓+𝕓)))^2))}},{{.75((((rs3 (ø+𝕒-2 𝕒2)-𝕒𝕓+𝕓))^2)+(((ø-𝕒-rs3 (-2 𝕒2𝕓+𝕒𝕓+𝕓)))^2))}}});

toPol[{a_,b_,c_,d_,e_,f_},"C3C4c"]:=Module[{f1=a-b+(d+e-2f)/(Sqrt[3]),f2=(a+b-2c)/(Sqrt[3])-d+e,f3=a-b-(d+e-2f)/(Sqrt[3]),f4=(a+b-2c)/(Sqrt[3])+d-e},{(((a+b+c))^2)+(((d+e+f))^2)(*ϵϵ*),If[d+e+f==0,If[a+b+c<0,π,0],ArcTan[a+b+c,d+e+f]](*σ*),
Expand[3((f1^2)+(f2^2))/4](*ηη*),If[f2==0,If[f1<0,π,0],ArcTan[f1,f2]]-π/6(*ϰ*),
Expand[3((f3^2)+(f4^2))/4](*κκ*),If[f4==0,If[f3<0,π,0],ArcTan[f3,f4]]-π/6(*ψ*)}]
toVec[{ϵϵ_,σ_,ηη_,χ_,κκ_,ψ_},"C3C4c"]:=Module[{ϵ=(Sqrt[ϵϵ])/3,η=(Sqrt[ηη/12]),κ=(Sqrt[κκ/12]),x=χ+π/6,y=ψ+π/6},
{(*a*)ϵ Cos[σ]+η Cos[x]+η rs3 Sin[x]+κ Cos[y]+κ rs3 Sin[y],
(*b*)ϵ Cos[σ]-η Cos[x]+η rs3 Sin[x]-κ Cos[y]+κ rs3 Sin[y],
(*c*)ϵ Cos[σ]-η 2rs3 Sin[x]-κ 2rs3 Sin[y],
(*d*)ϵ Sin[σ]+η rs3 Cos[x]-η Sin[x]-κ rs3 Cos[y]+κ Sin[y],
(*e*)ϵ Sin[σ]+η rs3 Cos[x]+η Sin[x]-κ rs3 Cos[y]-κ Sin[y],
(*f*)ϵ Sin[σ]-η 2rs3 Cos[x]+κ 2rs3 Cos[y]}]

sd["Q12c"]:=(el=Take[el3,6];rofu={};gi={1,3,2,-4,-5,-6,1,2};gp={1,2,1,0.,1,0.};sh={{{(((ø+𝕒+𝕒2))^2)+(((𝕒2𝕓+𝕒𝕓+𝕓))^2)}},{{.5 ((((ø-𝕒))^2)+(((ø-𝕒2))^2)+(((𝕒-𝕒2))^2)+(((-𝕒2𝕓+𝕒𝕓))^2)+(((-𝕒2𝕓+𝕓))^2)+(((-𝕒𝕓+𝕓))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_},"Q12c"]:=Module[{abc=((((a-b))^2)+(((b-c))^2)+(((c-a))^2))/2,def=((((d-e))^2)+(((e-f))^2)+(((f-d))^2))/2},{(((a+b+c))^2)+(((d+e+f))^2),If[d+e+f===0,0,ArcTan[a+b+c,d+e+f]],abc+def,If[c==b,0,ArcTan[2 a-b-c,Sqrt[3](c-b)]],def,If[e==f,0,ArcTan[2 d-e-f,Sqrt[3](f-e)]]}]
toVec[{ϵϵ_,σ_,ηη_,χ_,κκ_,ψ_},"Q12c"]:=Module[{ϵ=(Sqrt[ϵϵ])/3,η=2(Sqrt[ηη-κκ])/3,κ=2(Sqrt[κκ])/3},{ ϵ Cos[σ]+η Cos[χ] ,
ϵ Cos[σ]+η Cos[χ+2 π/3],
ϵ Cos[σ]+η Cos[χ-2 π/3],
ϵ Sin[σ]+κ  Cos[ψ],
ϵ Sin[σ]+κ  Cos[ψ+2 π/3],
ϵ Sin[σ]+κ  Cos[ψ-2 π/3]}];

shQ12c={{{(((ø+𝕒+𝕒2))^2)+(((𝕒2𝕓+𝕒𝕓+𝕓))^2)}},{{.5 ((((ø-𝕒))^2)+(((ø-𝕒2))^2)+(((𝕒-𝕒2))^2)+(((-𝕒2𝕓+𝕒𝕓))^2)+(((-𝕒2𝕓+𝕓))^2)+(((-𝕒𝕓+𝕓))^2))}}}/.{𝕒2𝕓->aab,𝕒2->aa,𝕒𝕓->ab,𝕒->a,𝕓->b};

sd["Q12r"]:=(el=Take[el3,6];rofu={};gi={1,-2,-5,-4,-3,-6,1,2};gp={1,1,1,0.,1,0.};sh={{{(((ø-𝕒2+𝕒𝕓))^2)+(((𝕒+𝕒2𝕓-𝕓))^2)}},{{.5((((ø+𝕒2))^2)+(((𝕒-𝕒2𝕓))^2)+(((ø-𝕒𝕓))^2)+(((𝕒2+𝕒𝕓))^2)+(((𝕒+𝕓))^2)+(((𝕒2𝕓+𝕓))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_},"Q12r"]:=Module[{ace=((a+c)^2+(a-e)^2+(c+e)^2)/2,bdf=((b+d)^2+(d+f)^2+(b-f)^2)/2},{(((a-c+e))^2)+(((b-d+f))^2),If[b+f===d,0,ArcTan[a-c+e,b-d+f]],
ace+bdf,If[c==-e,0,ArcTan[2 a-e+c,Sqrt[3](-c-e)]],
bdf,If[d==-f,0,ArcTan[2 b+d-f,Sqrt[3](-d-f)]]}]
toVec[{ϵϵ_,σ_,ηη_,χ_,κκ_,ψ_},"Q12r"]:=Module[{ϵ=(Sqrt[ϵϵ])/3,η=2(Sqrt[ηη-κκ])/3,κ=2(Sqrt[κκ])/3},{  ϵ Cos[σ]+η Cos[χ] ,
  ϵ Sin[σ]+κ Cos[ψ],
-ϵ Cos[σ]-η Cos[χ-2 π/3],
-ϵ Sin[σ]-κ Cos[ψ-2 π/3],
 ϵ Cos[σ]+η Cos[χ+2 π/3],
 ϵ Sin[σ]+κ Cos[ψ+2 π/3]}];

shQ12r={{{(((ø-𝕒2+𝕒𝕓))^2)+(((𝕒+𝕒2𝕓-𝕓))^2)}},{{.5((((ø+𝕒2))^2)+(((𝕒-𝕒2𝕓))^2)+(((ø-𝕒𝕓))^2)+(((𝕒2+𝕒𝕓))^2)+(((𝕒+𝕓))^2)+(((𝕒2𝕓+𝕓))^2))}}}/.{𝕒2𝕓->aab,𝕒2->aa,𝕒𝕓->ab,𝕒->a,𝕓->b}

sd["D12r"]:=(el=Take[el3,6];rofu={};gi={1,2,-5,4,-3,6,1,1,2};gp={1,1,1,0.,1,0.};sh={{{ø-𝕒-𝕒2-𝕒2𝕓+𝕒𝕓+𝕓}},{{ø+𝕒-𝕒2+𝕒2𝕓+𝕒𝕓-𝕓}},{{.5 ((((ø+𝕒2))^2)-(((𝕒-𝕒2𝕓))^2)+(((ø-𝕒𝕓))^2)+(((𝕒2+𝕒𝕓))^2)-(((𝕒+𝕓))^2)-(((𝕒2𝕓+𝕓))^2))}}});

sd["Cl3r"]:=(el=Take[el3,6];rofu={};gp={1,1,1,0.,1,0.};gi={1,-3,-2,-4,6,5,1,1};sh={{{(((ø-𝕒+𝕒2))^2)+(((𝕒2𝕓-𝕒𝕓+𝕓))^2)}},{{-3 (((ø 𝕒2𝕓+𝕒 𝕒2𝕓+ø 𝕒𝕓-𝕒2 𝕒𝕓-𝕒 𝕓-𝕒2 𝕓))^2)+.25((((((ø+𝕒))^2)+(((ø-𝕒2))^2)+(((𝕒+𝕒2))^2)+(((𝕒2𝕓+𝕒𝕓))^2)+(((𝕒2𝕓-𝕓))^2)+(((𝕒𝕓+𝕓))^2)))^2)}}});

sd["Clm3r"]:=(el=Take[el3,6];rofu={};gp={1,1,1,0.,1,0.};gi={1,3,2,-4,-6,-5,1,1};sh={{{(((ø-𝕒-𝕒2))^2)+(((-𝕒2𝕓-𝕒𝕓+𝕓))^2)}},{{-3 (((-ø 𝕒2𝕓-𝕒 𝕒2𝕓+ø 𝕒𝕓+𝕒2 𝕒𝕓-𝕒 𝕓+𝕒2 𝕓))^2)+((((((ø+𝕒))^2)+(((𝕒-𝕒2))^2)+(((ø+𝕒2))^2)+(((-𝕒2𝕓+𝕒𝕓))^2)+(((𝕒2𝕓+𝕓))^2)+(((𝕒𝕓+𝕓))^2)))^2)/4}}});

9.9 Shapes, Polar-Vector, Hyperbolics, sh, toPol, toVec, tohyPol, tohyVec for 8 & 9 element loops.

sd["C8"]:=(el=Take[el2,8];rofu={};gi={1,8,7,6,5,4,3,2,1,1,1,1};gp={1,1,1,1,0.,1,0.};sh={{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{(((𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø-𝕓-𝕓𝕔+𝕔))^2)}},{{((((((𝕒𝕓-𝕒𝕓𝕔))^2)+(((𝕒-𝕒𝕔))^2)))^2)+4 ((-𝕒+𝕒𝕔) (𝕓-𝕓𝕔)+(𝕒𝕓-𝕒𝕓𝕔) (ø-𝕔)) ((𝕒𝕓-𝕒𝕓𝕔) (𝕓-𝕓𝕔)+(𝕒-𝕒𝕔) (ø-𝕔))+((((((𝕓-𝕓𝕔))^2)+(((ø-𝕔))^2)))^2)}}});
sd["C2C2C2"]:=(el=Take[el2,8];rofu={};gp={1,1,1,1,1,1,1,1};gi={1,2,3,4,5,6,7,8,1,1,1,1,1,1,1,1};sh={{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓𝕔-𝕔}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø+𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"C2C2C2"]:=
{a+b+c+d-e-f-g-h,a+b-c-d+e+f-g-h,
a-b+c-d+e-f+g-h,a-b-c+d-e+f+g-h,
a-b-c+d+e-f-g+h,a-b+c-d-e+f-g+h,
a+b-c-d-e-f+g+h,a+b+c+d+e+f+g+h};
toVec[{α_,β_,γ_,δ_,ϵ_,σ_,ζ_,θ_},"C2C2C2"]:=
{ α+β+γ+δ+ϵ +σ+ζ +θ,α+β-γ-δ-ϵ -σ+ζ +θ,
α-β+γ-δ-ϵ+σ-ζ+θ,α-β-γ+δ+ϵ-σ-ζ+θ,
-α+β+γ-δ+ϵ -σ-ζ +θ,-α+β-γ+δ-ϵ +σ-ζ +θ,
-α-β+γ+δ-ϵ -σ+ζ +θ,-α-β-γ-δ+ϵ +σ+ζ +θ}/8

sd["C4C2"]:=(el=Take[el2,8];rofu={};gi={1,4,3,2,5,8,7,6,1,1,1,1,1,1};gp={1,1,1,1,1,0.,1,0.};sh={{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔))^2)+(((ø-𝕓+𝕓𝕔-𝕔))^2)}},{{(((𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø-𝕓-𝕓𝕔+𝕔))^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"C4C2"]:={a+b+c+d+e+f+g+h,a-b+c-d+e-f+g-h,a+b+c+d-e-f-g-h,a-b+c-d-e+f-g+h,(((a-c-e+g))^2)+(((b-d-f+h))^2),
ArcTan[a-c-e+g,b-d-f+h],
(((a-c+e-g))^2)+(((b-d+f-h))^2),
ArcTan[a-c+e-g,b-d+f-h]};
toVec[{α_,β_,γ_,δ_,ϵϵ_,σ_,ζζ_,θ_},"C4C2"]:=Module[{ϵ=2(Sqrt[ϵϵ]),ζ=2(Sqrt[ζζ])},
{  α+β+γ+δ+ϵ Cos[σ]+ζ Cos[θ],α-β+γ-δ+ϵ Sin[σ]+ζ Sin[θ],
α+β+γ+δ-ϵ Cos[σ]-ζ Cos[θ],α-β+γ-δ-ϵ Sin[σ]-ζ Sin[θ],
α+β-γ-δ-ϵ Cos[σ]+ζ Cos[θ],α-β-γ+δ-ϵ Sin[σ]+ζ Sin[θ],
α+β-γ-δ+ϵ Cos[σ]-ζ Cos[θ],α-β-γ+δ+ϵ Sin[σ]-ζ Sin[θ]}/8]

sd["D8"]:=(el=Take[el2,8];rofu={};gi={1,2,7,4,5,6,3,8,1,1,1,1,2};gp={1,1,1,1,1,0.,1,0.};sh={{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{-(((𝕒𝕓-𝕒𝕓𝕔))^2)-(((𝕒-𝕒𝕔))^2)+(((𝕓-𝕓𝕔))^2)+(((ø-𝕔))^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"D8"]:={a+b+c+d+e+f+g+h,a+b-c-d+e+f-g-h,a-b+c-d+e-f+g-h,a-b-c+d+e-f-g+h,
(((a-e))^2)+(((c-g))^2)-(((b-f))^2)-(((d-h))^2),ArcTan[a-e,c-g],
(((b-f))^2)+(((d-h))^2),ArcTan[b-f,d-h]};
toVec[{α_,β_,γ_,δ_,ϵϵ_,σ_,ζζ_,θ_},"D8"]:=Module[{ϵ=4(Sqrt[ϵϵ+ζζ]),ζ=4(Sqrt[ζζ])},
{α+β+γ+δ+ϵ Cos[σ],α+β-γ-δ+ζ Cos[θ],α-β+γ-δ+ϵ Sin[σ],α-β-γ+δ+ζ Sin[θ],α+β+γ+δ-ϵ Cos[σ],α+β-γ-δ-ζ Cos[θ],α-β+γ-δ-ϵ Sin[σ],α-β-γ+δ-ζ Sin[θ]}]/8;

sd["Q8"]:=(el=Take[el2,8];rofu={};gi={1,6,7,8,5,2,3,4,1,1,1,1,2};gp={1,1,1,1,1,0.,1,0.};sh={{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{(((𝕒𝕓-𝕒𝕓𝕔))^2)+(((𝕒-𝕒𝕔))^2)+(((𝕓-𝕓𝕔))^2)+(((ø-𝕔))^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"Q8"]:={a+b+c+d+e+f+g+h,a-b+c-d+e-f+g-h,a-b-c+d+e-f-g+h,a+b-c-d+e+f-g-h,(((a-e))^2)+(((b-f))^2),ArcTan[a-e,b-f],(((c-g))^2)+(((d-h))^2),ArcTan[c-g,d-h]};toVec[{α_,β_,γ_,δ_,ϵϵ_,σ_,ζζ_,θ_},"Q8"]:={  α+β+γ+δ+4(Sqrt[ϵϵ]) Cos[σ],α-β-γ+δ+4(Sqrt[ϵϵ]) Sin[σ],α+β-γ-δ+4(Sqrt[ζζ]) Cos[θ],α-β+γ-δ+4(Sqrt[ζζ]) Sin[θ],α+β+γ+δ-4(Sqrt[ϵϵ]) Cos[σ],α-β-γ+δ-4(Sqrt[ϵϵ]) Sin[σ],α+β-γ-δ-4(Sqrt[ζζ]) Cos[θ],α-β+γ-δ-4(Sqrt[ζζ]) Sin[θ]}/8;

sd["Octr"]:=(el=Take[el2,8];rofu={};gi={1,-2,-3,-4,-5,-6,-7,-8,4};gp={1,0.,1,0.,1,0.,1,0.};
sh={{{(ø^2)+(𝕒^2)+((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕔)^2)+(𝕓^2)+((𝕓𝕔)^2)+(𝕔^2)}}};
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"Octr"]:=Module[{},{(a^2)+(b^2)+(c^2)+(d^2)+(e^2)+(f^2)+(g^2)+(h^2),ArcTan[a,b],(c^2)+(d^2),ArcTan[c,d],(e^2)+(f^2),ArcTan[e,f],(g^2)+(h^2),ArcTan[g,h]}];
toVec[{pp_,ϕ_,qq_,ψ_,rr_,ρ_,ss_,σ_},"Octr"]:=Module[{p=(Sqrt[pp-qq-rr-ss]),q=(Sqrt[qq]),r=(Sqrt[rr]),s=(Sqrt[ss])},{  p Cos[ϕ] ,p Sin[ϕ],q Cos[ψ] ,q Sin[ψ] ,r Cos[ρ] ,r Sin[ρ],s Cos[σ],s Sin[σ]}]);

shOctr={(ø^2)+(𝕒^2)+((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕔)^2)+(𝕓^2)+((𝕓𝕔)^2)+(𝕔^2)}/.{𝕒𝕓𝕔->abc,𝕒2𝕓->aab,𝕒2->aa,𝕒𝕔->ac,𝕓𝕔->bc,𝕒𝕓->ab,𝕒->a,𝕓->b,𝕔->c}

sd["Octi"]:=(el=Take[el2,8];rofu={};gp={1,0.,1,0.,1,0.,1,0.};gi={1,2,-3,4,-5,6,-7,8,4};
sh={{{(ø^2)-(𝕒^2)-((𝕒𝕓)^2)-((𝕒𝕓𝕔)^2)-((𝕒𝕔)^2)+(𝕓^2)+((𝕓𝕔)^2)+(𝕔^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"Octi"]:=Module[{},{(a^2)+(c^2),ArcTan[a,c],(b^2)+(d^2),ArcTan[b,d],(e^2)+(g^2),ArcTan[e,g],(f^2)+(h^2),ArcTan[f,h]}];toVec[{pp_,ϕ_,qq_,ψ_,rr_,ρ_,ss_,σ_},"Octi"]:=Module[{p=Sqrt[pp],q=Sqrt[qq],r=Sqrt[rr],s=Sqrt[ss]},{p Cos[ϕ] ,q Cos[ψ],p Sin[ϕ] ,q Sin[ψ] ,r Cos[ρ] ,s Cos[σ],r Sin[ρ],s Sin[σ]}];

shOcti={(ø^2)-(𝕒^2)-((𝕒𝕓)^2)-((𝕒𝕓𝕔)^2)-((𝕒𝕔)^2)+(𝕓^2)+((𝕓𝕔)^2)+(𝕔^2)}/.{𝕒𝕓𝕔->abc,𝕒2𝕓->aab,𝕒2->aa,𝕒𝕔->ac,𝕓𝕔->bc,𝕒𝕓->ab,𝕒->a,𝕓->b,𝕔->c}

sd["KiC4c"]:=(el=Take[el2,8];rofu={};gi={1,2,3,4,-5,-8,-7,-6,1,1,2};gp={1,0.,1,0.,1,0,1,0.};sh={{{(((ø-𝕒-𝕒𝕓+𝕓))^2)+(((-𝕒𝕓𝕔-𝕒𝕔+𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒+𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕒𝕔+𝕓𝕔+𝕔))^2)}},{{-(((𝕒-𝕒𝕓))^2)-(((-𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø-𝕓))^2)+(((-𝕓𝕔+𝕔))^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"KiC4c"]:=Module[{},{(*pp*)(((a-c))^2)-(((b-d))^2)+(((e-g))^2)-(((f-h))^2),(*ϕ*)If[e==g,0,ArcTan[a-c,e-g]],
(*qq*)(((b-d))^2)+(((f-h))^2),
(*ψ*)If[f==h,0,ArcTan[b-d,f-h]],(*rr*)(((a-b+c-d))^2)+(((e-f+g-h))^2),(*ρ*)If[e+g==f+h,0,ArcTan[a-b+c-d,e-f+g-h]],(*ss*)(((a+b+c+d))^2)+(((e+f+g+h))^2),(*σ*)If[e+f==g+h,0,ArcTan[a+b+c+d,e+f+g+h]]}]
toVec[{pp_,ϕ_,qq_,ψ_,rr_,ρ_,ss_,σ_},"KiC4c"]:=Module[{p=(Sqrt[pp+qq])/2,q=(Sqrt[qq])/2,r=(Sqrt[rr])/4,s=(Sqrt[ss])/4},{(*a*)  p Cos[ϕ] +r Cos[ρ]+s Cos[σ],
   (*b*) +q Cos[ψ]-r Cos[ρ]+s Cos[σ],
(*c*)-p Cos[ϕ]+r Cos[ρ]+s Cos[σ] ,
   (*d*)-q Cos[ψ]-r Cos[ρ]+s Cos[σ],
(*e*)  p Sin[ϕ]+r Sin[ρ]+s Sin[σ],
   (*f*)+q Sin[ψ]-r Sin[ρ]+s Sin[σ],
(*g*)-p Sin[ϕ]+r Sin[ρ]+s Sin[σ],
   (*h*) -q Sin[ψ]-r Sin[ρ]+s Sin[σ]}];

sd["O4"]:=(el=Take[el2,8];rofu={};gp={1,0.,1,0.,1,0.,1,0.};gi={1,2,3,4,-5,-6,-7,-8,1,1,1,1};
sh={{{(((ø-𝕒+𝕒𝕓-𝕓))^2)+(((𝕒𝕓𝕔-𝕒𝕔-𝕓𝕔+𝕔))^2)}},{{(((ø-𝕒-𝕒𝕓+𝕓))^2)+(((-𝕒𝕓𝕔-𝕒𝕔+𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒-𝕒𝕓-𝕓))^2)+(((-𝕒𝕓𝕔+𝕒𝕔-𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒+𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕒𝕔+𝕓𝕔+𝕔))^2)}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"O4"]:=Module[{},gp={1,0.,1,0.,1,0.,1,0.};{(((a-b-c+d))^2)+(((e-f-g+h))^2),If[e+h==f+g,0,ArcTan[a-b-c+d,e-f-g+h]],(((a-b+c-d))^2)+(((e-f+g-h))^2),If[e+g==f+h,0,ArcTan[a-b+c-d,e-f+g-h]],(((a+b-c-d))^2)+(((e+f-g-h))^2),If[e+f==g+h,0,ArcTan[a+b-c-d,e+f-g-h]],(((a+b+c+d))^2)+(((e+f+g+h))^2),If[e+f+g+h==0,0,ArcTan[a+b+c+d,e+f+g+h]]}];
toVec[{pp_,ϕ_,qq_,ψ_,rr_,ρ_,ss_,σ_},"O4"]:=Module[{p=Sqrt[pp],q=Sqrt[qq],r=Sqrt[rr],s=Sqrt[ss]},{  p Cos[ϕ] +q Cos[ψ] +r Cos[ρ] +s Cos[σ],- p Cos[ϕ]-q Cos[ψ]+r Cos[ρ] +s Cos[σ],-p Cos[ϕ] +q Cos[ψ] -r Cos[ρ] +s Cos[σ], p Cos[ϕ]-q Cos[ψ] -r Cos[ρ] +s Cos[σ],
  p Sin[ϕ] +q Sin[ψ] +r Sin[ρ] +s Sin[σ],-p Sin[ϕ]-q Sin[ψ] +r Sin[ρ] +s Sin[σ],
-p Sin[ϕ] +q Sin[ψ] -r Sin[ρ] +s Sin[σ], p Sin[ϕ] -q Sin[ψ]-r Sin[ρ]+s Sin[σ]}]/4

sd["O4a"]:=(el=Take[el2,8];rofu={};gp={1,0.,1,0.,1,0.,1,0.};gi={1,-2,3,-4,-5,6,-7,8,1,1,1,1};
sh={{{(((ø+𝕒𝕓𝕔-𝕒𝕔-𝕓))^2)+(((𝕒-𝕒𝕓-𝕓𝕔+𝕔))^2)}},{{(((ø-𝕒𝕓𝕔+𝕒𝕔-𝕓))^2)+(((𝕒-𝕒𝕓+𝕓𝕔-𝕔))^2)}},{{(((ø-𝕒𝕓𝕔-𝕒𝕔+𝕓))^2)+(((𝕒+𝕒𝕓+𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒𝕓𝕔+𝕒𝕔+𝕓))^2)+(((𝕒+𝕒𝕓-𝕓𝕔-𝕔))^2)}}});
sd["O4b"]:=(gp={1,0.,1,0.,1,0.,1,0.};el=Take[el2,8];rofu={};gi={1,-2,-3,4,-5,6,7,-8,1,1,1,1};
sh={{{(((-ø+𝕒𝕓+𝕒𝕔+𝕓𝕔))^2)+(((𝕒-𝕒𝕓𝕔+𝕓+𝕔))^2)}},{{(((ø-𝕒𝕓+𝕒𝕔+𝕓𝕔))^2)+(((𝕒+𝕒𝕓𝕔+𝕓-𝕔))^2)}},{{(((ø+𝕒𝕓-𝕒𝕔+𝕓𝕔))^2)+(((𝕒+𝕒𝕓𝕔-𝕓+𝕔))^2)}},{{(((ø+𝕒𝕓+𝕒𝕔-𝕓𝕔))^2)+(((-𝕒+𝕒𝕓𝕔+𝕓+𝕔))^2)}}});

sd["C4C4c"]:=(el=Take[el2,8];rofu={};gp={1,0.,1,0.,1,0.,1,0.};gi={1,4,3,2,-5,-8,-7,-6,1,1,1,1};sh={{{(((ø+𝕒𝕓𝕔-𝕒𝕔-𝕓))^2)+(((𝕒-𝕒𝕓-𝕓𝕔+𝕔))^2)}},{{(((ø-𝕒𝕓𝕔+𝕒𝕔-𝕓))^2)+(((𝕒-𝕒𝕓+𝕓𝕔-𝕔))^2)}},{{(((ø-𝕒-𝕒𝕓+𝕓))^2)+(((-𝕒𝕓𝕔-𝕒𝕔+𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒+𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕒𝕔+𝕓𝕔+𝕔))^2)}}});toPol[{a_,b_,c_,d_,e_,f_,g_,h_},"C4C4c"]:=Module[{aa,bb,ss,w},ss:=aa^2+bb^2;
w:=Which[bb===0&&aa<0,π,bb==0,0,aa==0,π/2 Sign[bb],True,ArcTan[aa,bb]];{aa=a-c-f+h;bb=b-d+e-g;ss,w,aa=a-c+f-h;bb=b-d-e+g;ss,w,aa=a-b+c-d;bb=e-f+g-h;ss,w,aa=a+b+c+d;bb=e+f+g+h;ss,w}];
toVec[{pp_,ϕ_,qq_,ψ_,rr_,ρ_,ss_,σ_},"C4C4c"]:=Module[{p=Sqrt[pp],q=Sqrt[qq],r=Sqrt[rr],s=Sqrt[ss]},{    p Cos[ϕ]+q Cos[ψ]+r Cos[ρ]+s Cos[σ],
 p Sin[ϕ]+q Sin[ψ]-r Cos[ρ]+s Cos[σ],
-p Cos[ϕ]-q Cos[ψ]+r Cos[ρ]+s Cos[σ],-p Sin[ϕ]-q Sin[ψ]-r Cos[ρ]+s Cos[σ],
  p Sin[ϕ]-q Sin[ψ]+r Sin[ρ]+s Sin[σ],-p Cos[ϕ]+q Cos[ψ]-r Sin[ρ]+s Sin[σ],
-p Sin[ϕ]+q Sin[ψ]+r Sin[ρ]+s Sin[σ],  p Cos[ϕ]-q Cos[ψ]-r Sin[ρ]+s Sin[σ]}/4];

sd["C4C4r"]:=(el=Take[el2,8];rofu={};gp={1,0.,1,0.,1,0.,1,0.};gi={1,-4,3,-2,-5,8,-7,6,1,1,1,1};sh={{{(((ø-𝕒𝕓𝕔-𝕒𝕔+𝕓))^2)+(((𝕒+𝕒𝕓+𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒-𝕒𝕓-𝕓))^2)+(((-𝕒𝕓𝕔+𝕒𝕔-𝕓𝕔+𝕔))^2)}},{{(((ø-𝕒+𝕒𝕓-𝕓))^2)+(((𝕒𝕓𝕔-𝕒𝕔-𝕓𝕔+𝕔))^2)}},{{(((ø+𝕒𝕓𝕔+𝕒𝕔+𝕓))^2)+(((𝕒+𝕒𝕓-𝕓𝕔-𝕔))^2)}}});

sd["Q8C2r"]:=(el=Take[el2,8];rofu={};gi={1,3,2,-7,5,-8,-4,-6,1,1,1,1,2};gp={1,1,1,1,1,0.,1,0.};sh={{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔-𝕔}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔-𝕔}},{{(((𝕒𝕓𝕔+𝕒𝕔))^2)+(((𝕒-𝕓))^2)+(((𝕒𝕓+𝕓𝕔))^2)+(((ø+𝕔))^2)}}});

sd["C2D4r"]:=(el=Take[el2,8];rofu={};gi={1,2,3,4,-5,-6,7,8,2,2};gp={1,0.,1,0.,1,0.,1,0.};sh={{{(((ø+𝕒))^2)-(((𝕒𝕓+𝕓))^2)-(((𝕒𝕓𝕔+𝕓𝕔))^2)+(((𝕒𝕔+𝕔))^2)}},{{(((ø-𝕒))^2)-(((-𝕒𝕓+𝕓))^2)-(((-𝕒𝕓𝕔+𝕓𝕔))^2)+(((-𝕒𝕔+𝕔))^2)}}});

sd["P8"]:=(el=Take[el2,8];rofu={};gi={1,2,3,4,5,6,7,8,2,2};gp={1,0.,1,0.,1,0.,1,0.};
sh={{{-(((𝕒𝕓+𝕒𝕓𝕔))^2)-(((𝕒+𝕒𝕔))^2)-(((𝕓+𝕓𝕔))^2)+(((ø+𝕔))^2)}},{{-(((𝕒𝕓-𝕒𝕓𝕔))^2)-(((𝕒-𝕒𝕔))^2)-(((𝕓-𝕓𝕔))^2)+(((ø-𝕔))^2)}}});

sd["CL3"]:=(el=Take[el2,8];rofu={};gi={1,2,3,-4,5,-6,-7,-8,2,2};gp={};
sh={{{4 (((ø 𝕒𝕓𝕔+𝕒𝕔 𝕓-𝕒 𝕓𝕔-𝕒𝕓 𝕔))^2)+((((ø^2)-(𝕒^2)+((𝕒𝕓)^2)-((𝕒𝕓𝕔)^2)+((𝕒𝕔)^2)-(𝕓^2)+((𝕓𝕔)^2)-(𝕔^2)))^2)}}});
sd["CL30"]:=(el=Take[el2,8];rofu={};gi={1,2,3,-4,5,-6,-7,-8,2,2}; gp={};
sh={{{(((ø+I 𝕒𝕓𝕔))^2)-(((I 𝕒𝕔-𝕓))^2)-(((𝕒+I 𝕓𝕔))^2)+(((𝕒𝕓-I 𝕔))^2)}},{{(((ø-I 𝕒𝕓𝕔))^2)-(((I 𝕒𝕔+𝕓))^2)-(((𝕒-I 𝕓𝕔))^2)+(((𝕒𝕓+I 𝕔))^2)}}});sd["CL12"]:=(el=Take[el2,8];rofu={};gi={1,2,-3,4,-5,6,-7,-8,2,2};gp={};sh={{{(((ø+I 𝕒𝕓𝕔))^2)+(((I 𝕒𝕔+𝕓))^2)-(((𝕒+I 𝕓𝕔))^2)-(((𝕒𝕓+I 𝕔))^2)}},{{(((ø-I 𝕒𝕓𝕔))^2)+(((-I 𝕒𝕔+𝕓))^2)-(((𝕒-I 𝕓𝕔))^2)-(((𝕒𝕓-I 𝕔))^2)}}});
sd["CL21"]:=(el=Take[el2,8];rofu={};gi={1,2,3,-4,-5,6,7,8,2,2};gp={};
sh={{{(((ø-𝕒𝕓𝕔))^2)-(((𝕒𝕔+𝕓))^2)-(((𝕒-𝕓𝕔))^2)+(((𝕒𝕓+𝕔))^2)}},{{(((ø+𝕒𝕓𝕔))^2)-(((-𝕒𝕔+𝕓))^2)-(((𝕒+𝕓𝕔))^2)+(((𝕒𝕓-𝕔))^2)}}});sd["CL03"]:=(el=Take[el2,8];rofu={};gi={1,-2,-3,-4,-5,-6,-7,8,2,2};gp={};
sh={{{(((ø-𝕒𝕓𝕔))^2)+(((-𝕒𝕔+𝕓))^2)+(((𝕒+𝕓𝕔))^2)+(((𝕒𝕓+𝕔))^2)}},{{(((ø+𝕒𝕓𝕔))^2)+(((𝕒𝕔+𝕓))^2)+(((𝕒-𝕓𝕔))^2)+(((𝕒𝕓-𝕔))^2)}}});
sd["C4iC4c"]:=(el=Take[el2,8];rofu={};gi={1,4,3,2,-5,-6,-7,-8,2,1,1};gp={1,1,2,1,0.,1,0.};sh={{{(((𝕒-𝕒𝕓))^2)+(((𝕒𝕓𝕔-𝕒𝕔))^2)+(((ø-𝕓))^2)+(((𝕓𝕔-𝕔))^2)}},{{(((ø-𝕒-𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕒𝕔-𝕓𝕔-𝕔))^2)}},{{(((ø+𝕒+𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕒𝕔+𝕓𝕔+𝕔))^2)}}});
sd["QC2r"]:=(el=Take[el2,8];rofu={};gi={1,2,-3,-4,-5,-6,-7,-8,2,2};gp={1,1,1,1,0.,1,0.};sh={{{(((ø-𝕒))^2)+(((𝕒𝕓-𝕓))^2)+(((𝕒𝕓𝕔-𝕓𝕔))^2)+(((𝕒𝕔-𝕔))^2)}},{{(((ø+𝕒))^2)+(((𝕒𝕓+𝕓))^2)+(((𝕒𝕓𝕔+𝕓𝕔))^2)+(((𝕒𝕔+𝕔))^2)}}});
sd["KiC4r"]:=(el=Take[el2,8];rofu={};gp={1,1,1,1,0.,1,0.};gi={1,2,-3,-8,5,6,-7,-4,2,1,1};sh={{{-(((𝕒𝕓-𝕒𝕓𝕔))^2)-(((𝕒-𝕒𝕔))^2)+(((𝕓-𝕓𝕔))^2)+(((ø-𝕔))^2)}},{{(((-𝕒𝕓-𝕒𝕓𝕔+𝕓+𝕓𝕔))^2)+(((ø+𝕒+𝕒𝕔+𝕔))^2)}},{{(((𝕒𝕓+𝕒𝕓𝕔+𝕓+𝕓𝕔))^2)+(((ø-𝕒-𝕒𝕔+𝕔))^2)}}});

sd["C3C3"]:=(gp={1,1,0.,1,0.,1,0.,1,0.};gi={1,3,2,7,9,8,4,6,5,1,1,1,1,1};el=Take[el3,9];rofu={};sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕔+𝕒𝕓+𝕒𝕔+𝕓+𝕔}},{{.5 ((((ø-𝕒+𝕒2𝕓-𝕒2𝕔+𝕒𝕔-𝕓))^2)+(((𝕒-𝕒2+𝕒2𝕔-𝕒𝕓+𝕓-𝕔))^2)+(((-ø+𝕒2-𝕒2𝕓+𝕒𝕓-𝕒𝕔+𝕔))^2))}},{{.5 ((((ø-𝕒2+𝕒2𝕔+𝕒𝕓-𝕒𝕔-𝕓))^2)+(((ø-𝕒-𝕒2𝕓+𝕒2𝕔+𝕒𝕓-𝕔))^2)+(((𝕒-𝕒2+𝕒2𝕓-𝕒𝕔-𝕓+𝕔))^2))}},{{.5 ((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕔+𝕒𝕓+𝕒𝕔))^2)+(((-ø+𝕒2+𝕒2𝕓+𝕒2𝕔-𝕓-𝕔))^2)+(((ø-𝕒-𝕒𝕓-𝕒𝕔+𝕓+𝕔))^2))}},{{.5 ((((ø+𝕒+𝕒2-𝕒2𝕓-𝕒𝕓-𝕓))^2)+(((ø+𝕒+𝕒2-𝕒2𝕔-𝕒𝕔-𝕔))^2)+(((𝕒2𝕓-𝕒2𝕔+𝕒𝕓-𝕒𝕔+𝕓-𝕔))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_},"C3C3"]:={a+b+c+d+e+f+g+h+i,((((a-b-d+f+h-i))^2)+(((b-c+d-e+i-g))^2)+(((-a+c+e-f+g-h))^2))/2,
ArcTan[2 a-b-c-d-e+2 f-g+2 h-i,-Sqrt[3](b-c+d-e+i-g)],
((((a-b+e-f-g+i))^2)+(((b-c-d+f+g-h))^2)+(((a-c-d+e-h+i))^2))/2,
ArcTan[2 a-b-c-d+2 e-f-g-h+2 i,-Sqrt[3](b-c-d+f+g-h)],
((((a-b+d-e+g-h))^2)+(((b-c+e-f+h-i))^2)+(((c-a+f-d+i-g))^2))/2,
ArcTan[2 a-b-c+2 d-e-f+2 g-h-i,-Sqrt[3](b-c+e-f+h-i)],
((((a+b+c-d-e-f))^2)+(((d+e+f-g-h-i))^2)+(((a+b+c-g-h-i))^2))/2,
ArcTan[2 a+2 b+2 c-d-e-f-g-h-i,-Sqrt[3](d+e+f-g-h-i)]};
toVec[{α_,ζ2_,θ_,η2_,ϑ_,κ2_,ϰ_,λ2_,ϕ_},"C3C3"]:=Module[{ζ=(Sqrt[ζ2]),η=(Sqrt[η2]),κ=(Sqrt[κ2]),λ=(Sqrt[λ2])},
{  α+2ζ Cos[θ]               +2η Cos[ϑ]                +2κ Cos[ϰ]               +2λ Cos[ϕ], α+2ζ Cos[θ+2π/3]+2η Cos[ϑ+2π/3]+2κ Cos[ϰ+2π/3]+2λ Cos[ϕ],
α+2ζ Cos[θ+4π/3]+2η Cos[ϑ+4π/3]+2κ Cos[ϰ+4π/3]+2λ Cos[ϕ],α+2ζ Cos[θ+2π/3]+2η Cos[ϑ+4π/3]+2κ Cos[ϰ]               +2λ Cos[ϕ+2π/3],
α+2ζ Cos[θ+4π/3]+2η Cos[ϑ]               +2κ Cos[ϰ+2π/3]+2λ Cos[ϕ+2π/3], α+2ζ Cos[θ]               +2η Cos[ϑ+2π/3]+2κ Cos[ϰ+4π/3]+2λ Cos[ϕ+2π/3],
α+2ζ Cos[θ+4π/3]+2η Cos[ϑ+2π/3]+2κ Cos[ϰ]               +2λ Cos[ϕ+4π/3], α+2ζ Cos[θ]               +2η Cos[ϑ+4π/3]+2κ Cos[ϰ+2π/3]+2λ Cos[ϕ+4π/3], α+2ζ Cos[θ+2π/3]+2η Cos[ϑ]               +2κ Cos[ϰ+4π/3]+2λ Cos[ϕ+4π/3]}/9];

sd["C6C3c"]:=(gp={1,1,1,1,1,1,0.,1,0.,1,0.,1,0.};gi={1,3,2,9,8,7,6,5,4,1,1,1,1,1};el=Take[el3,9];rofu={};sh={{{ø+𝕒+𝕒2+𝕒2𝕓-𝕒2𝕔+𝕒𝕓+𝕒𝕔-𝕓+𝕔}},{{.5 ((((ø+𝕒+𝕒2-𝕒2𝕓-𝕒𝕓+𝕓))^2)+(((ø+𝕒+𝕒2+𝕒2𝕔-𝕒𝕔-𝕔))^2)+(((𝕒2𝕓+𝕒2𝕔+𝕒𝕓-𝕒𝕔-𝕓-𝕔))^2))}},
{{.5((((ø-𝕒-𝕒2𝕓+𝕒2𝕔+𝕒𝕓+𝕒𝕔))^2)+(((𝕒-𝕒2+𝕒2𝕓-𝕒2𝕔+𝕓-𝕔))^2)+(((ø-𝕒2+𝕒𝕓+𝕒𝕔+𝕓-𝕔))^2))}},{{.5 ((((𝕒-𝕒2+𝕒2𝕔-𝕒𝕓+𝕒𝕔-𝕓))^2)+(((ø-𝕒2+𝕒2𝕓+𝕒2𝕔-𝕒𝕓+𝕔))^2)+(((ø-𝕒+𝕒2𝕓-𝕒𝕔+𝕓+𝕔))^2))}},{{.5 ((((ø-𝕒2-𝕒2𝕓-𝕒2𝕔-𝕒𝕔-𝕓))^2)+(((ø-𝕒-𝕒2𝕔-𝕒𝕓-𝕓-𝕔))^2)+(((𝕒-𝕒2-𝕒2𝕓+𝕒𝕓-𝕒𝕔+𝕔))^2))}}});

9.10 Shapes, Polar-Vector, Hyperbolics, sh, toPol, toVec, tohyPol, tohyVec for 12 element loops.

sd["C12"]:=(el=Take[el3,12];rofu={};
gi={1,3,2,10,12,11,7,9,8,4,6,5,1,1,1,1,1,1,1};
gp={1,1,1,0.,1,0.,1,0.,1,0.,1,0.};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},
{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},
{{(((𝕒2𝕓-𝕒2𝕓𝕔+𝕒𝕓-𝕒𝕓𝕔+𝕓-𝕓𝕔))^2)+(((ø+𝕒+𝕒2-𝕒2𝕔-𝕒𝕔-𝕔))^2)}}, 
{{.5((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔))^2)+
(((-ø+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔-𝕓-𝕓𝕔-𝕔))^2)+
(((ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2))}},
{{.5((((𝕒-𝕒2+𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+
(((-ø+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔+𝕓+𝕓𝕔-𝕔))^2)+
(((ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔))^2))}},
{{.75((((𝕒𝕓-𝕒𝕓𝕔-𝕓+𝕓𝕔+rs3 (ø+𝕒-2 𝕒2+2 𝕒2𝕔-𝕒𝕔-𝕔)))^2)+
(((ø-𝕒+𝕒𝕔+rs3 (-2 𝕒2𝕓+2 𝕒2𝕓𝕔+𝕒𝕓-𝕒𝕓𝕔+𝕓-𝕓𝕔)-𝕔))^2))}},
{{.75((((-𝕒𝕓+𝕒𝕓𝕔+𝕓-𝕓𝕔+rs3 (ø+𝕒-2 𝕒2+2 𝕒2𝕔-𝕒𝕔-𝕔)))^2)+
(((ø-𝕒+𝕒𝕔-rs3 (-2 𝕒2𝕓+2 𝕒2𝕓𝕔+𝕒𝕓-𝕒𝕓𝕔+𝕓-𝕓𝕔)-𝕔))^2))}}});

toVec[{α_,β_,ϵϵ_,σ_,ζζ_,τ_,λλ_,ϕ_,ηη_,χ_,κκ_,ψ_},"C12"]:=
Module[{ϵ=2(Sqrt[ϵϵ]),ζ=2(Sqrt[ζζ]),λ=2(Sqrt[λλ]),η=(Sqrt[3ηη]),κ=(Sqrt[3κκ]),x=χ+π/6,y=ψ+π/6},
{α+β+ϵ Cos[σ]+ζ Cos[τ]+λ Cos[ϕ]+η Cos[x]+η rs3 Sin[x]+κ Cos[y]+κ rs3 Sin[y],
α+β+ϵ Cos[σ]+ζ Cos[τ+ω]+λ Cos[ϕ+ω]-η Cos[x]+η rs3 Sin[x]-κ Cos[y]+κ rs3 Sin[y],
α+β+ϵ Cos[σ]+ζ Cos[τ-ω]+λ Cos[ϕ-ω]-2η rs3 Sin[x]-2κ rs3 Sin[y],
α-β+ϵ Sin[σ]+ζ Cos[τ]-λ Cos[ϕ]+η rs3 Cos[x]-η Sin[x]-κ rs3 Cos[y]+κ Sin[y],
α-β+ϵ Sin[σ]+ζ Cos[τ+ω]-λ Cos[ϕ+ω]+η rs3 Cos[x]+η Sin[x]-κ rs3 Cos[y]-κ Sin[y],
α-β+ϵ Sin[σ]+ζ Cos[τ-ω]-λ Cos[ϕ-ω]-2η rs3 Cos[x]+2κ rs3 Cos[y],
α+β-ϵ Cos[σ]+ζ Cos[τ]+λ Cos[ϕ]-η Cos[x]-η rs3 Sin[x]-κ Cos[y]-κ rs3 Sin[y],
α+β-ϵ Cos[σ]+ζ Cos[τ+ω]+λ Cos[ϕ+ω]+η Cos[x]-η rs3 Sin[x]+κ Cos[y]-κ rs3 Sin[y],
α+β-ϵ Cos[σ]+ζ Cos[τ-ω]+λ Cos[ϕ-ω]+2η rs3 Sin[x]+2κ rs3 Sin[y],
α-β-ϵ Sin[σ]+ζ Cos[τ]-λ Cos[ϕ]-η rs3 Cos[x]+η Sin[x]+κ rs3 Cos[y]-κ Sin[y],
α-β-ϵ Sin[σ]+ζ Cos[τ+ω]-λ Cos[ϕ+ω]-η rs3 Cos[x]-η Sin[x]+κ rs3 Cos[y]+κ Sin[y],
α-β-ϵ Sin[σ]+ζ Cos[τ-ω]-λ Cos[ϕ-ω]+2η  rs3 Cos[x]-2κ rs3 Cos[y]}/12];

toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_},"C12"]:=
Module[{ϵ,e1=a+b+c-g-h-i,e2=d+e+f-j-k-l,a1=a-b+d-e+g-h+j-k,a2=a-b-d+e+g-h-j+k,
b1=Chop[FullSimplify[b-c+e-f+h-i+k-l]],b2=Chop[FullSimplify[b-c-e+f+h-i-k+l]],
c1=c-a+f-d+i-g+l-j,c2=c-a-f+d+i-g-l+j,f1=a-b-g+h+(d+e-2 f-j-k+2l)rs3,
f2=(a+b-2c-g-h+2i)rs3-d+e+j-k,
f3=a-b-g+h-(d+e-2 f-j-k+2l)rs3,
f4=(a+b-2c-g-h+2i)rs3+d-e-j+k},
Chop[{a+b+c+d+e+f+g+h+i+j+k+l,a+b+c-d-e-f+g+h+i-j-k-l,
ϵ=(e1^2)+(e2^2),If[ϵ==0&&e2==0,0,ArcTan[e1,e2],ArcTan[e1,e2]],
((a1^2)+(b1^2)+(c1^2))/2,If[b1==0,0,ArcTan[a1-c1,rs3 b1]],
((a2^2)+(b2^2)+(c2^2))/2,If[b2==0,0,ArcTan[a2-c2,rs3 b2]],
((f1^2)+(f2^2))3/4,If[f2==0,-π/6,ArcTan[f1,f2]-π/6],
((f3^2)+(f4^2))3/4,If[f4==0,-π/6,ArcTan[f3,f4]-π/6]}]];

sd["C6C2"]:=(el=Take[el3,12];rofu={};
gi={1,3,2,4,6,5,7,9,8,10,12,11,1,1,1,1,1,1,1,1};
gp={1,1,1,1,1,0.,1,0.,1,0.,1,0.};

sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},
{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},
{{ø+𝕒+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔}},
{{ø+𝕒+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔}},
{{.5((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔))^2)+
(((-ø+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔-𝕓-𝕓𝕔-𝕔))^2)+
(((ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2))}},
{{.5 ((((𝕒-𝕒2+𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+
(((-ø+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔+𝕓+𝕓𝕔-𝕔))^2)+
(((ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔))^2))}},
{{.5((((𝕒-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔))^2)+
(((ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔-𝕔))^2)+
(((-ø+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔-𝕓+𝕓𝕔+𝕔))^2))}},
{{.5((((𝕒-𝕒2+𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔))^2)+
(((ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓𝕔-𝕔))^2)+
(((-ø+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔+𝕓-𝕓𝕔+𝕔))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_},"C6C2"]:=
Module[{r=-Sqrt[3],a1=a-b+d-e+g-h+j-k,a2=a-b-d+e+g-h-j+k,
a3=a-b+d-e-g+h-j+k,a4=a-b-d+e-g+h+j-k,
b1=Chop[FullSimplify[b-c+e-f+h-i+k-l]],b2=Chop[FullSimplify[b-c-e+f+h-i-k+l]],
b3=Chop[FullSimplify[b-c+e-f-h+i-k+l]],b4=Chop[FullSimplify[b-c-e+f-h+i+k-l]],
c1=c-a+f-d+i-g+l-j,c2=c-a-f+d+i-g-l+j,
c3=c-a+f-d-i+g-l+j,c4=c-a-f+d-i+g+l-j},
Chop[{a+b+c+d+e+f+g+h+i+j+k+l,a+b+c-d-e-f+g+h+i-j-k-l,
a+b+c+d+e+f-g-h-i-j-k-l,a+b+c-d-e-f-g-h-i+j+k+l,
((a1^2)+(b1^2)+(c1^2))/2,If[b1==0,0,ArcTan[a1-c1,r b1]],
((a2^2)+(b2^2)+(c2^2))/2,If[b2==0,0,ArcTan[a2-c2,r b2]],
((a3^2)+(b3^2)+(c3^2))/2,If[b3==0,0,ArcTan[a3-c3,r b3]],
((a4^2)+(b4^2)+(c4^2))/2,If[b4==0,0,ArcTan[a4-c4,r b4]]}]];

toVec[{α_,β_,γ_,δ_,ζζ_,τ_,λλ_,ϕ_,ηη_,χ_,κκ_,ψ_},"C6C2"]:=
Module[{ζ=2(Sqrt[ζζ]),λ=2(Sqrt[λλ]),η=2(Sqrt[ηη]),κ=2(Sqrt[κκ])},
{  α+β+γ+δ+ζ Cos[τ]      +λ Cos[ϕ]     +η Cos[χ]      +κ Cos[ψ],
α+β+γ+δ+ζ Cos[τ+ω]+λ Cos[ϕ+ω]+η Cos[χ+ω]+κ Cos[ψ+ω], 
α+β+γ+δ+ζ Cos[τ-ω]+λ Cos[ϕ-ω]+η Cos[χ-ω]+κ Cos[ψ-ω],
α-β+γ-δ+ζ Cos[τ]      -λ Cos[ϕ]     +η Cos[χ]      -κ Cos[ψ] ,
α-β+γ-δ+ζ Cos[τ+ω]-λ Cos[ϕ+ω]+η Cos[χ+ω]-κ Cos[ψ+ω],
α-β+γ-δ+ζ Cos[τ-ω]-λ Cos[ϕ-ω]+η Cos[χ-ω]-κ Cos[ψ-ω],
α+β-γ-δ+ζ Cos[τ]      +λ Cos[ϕ]     -η Cos[χ]      -κ Cos[ψ] ,
α+β-γ-δ+ζ Cos[τ+ω]+λ Cos[ϕ+ω]-η Cos[χ+ω]-κ Cos[ψ+ω],
α+β-γ-δ+ζ Cos[τ-ω]+λ Cos[ϕ-ω]-η Cos[χ-ω]-κ Cos[ψ-ω],
α-β-γ+δ+ζ Cos[τ]      -λ Cos[ϕ]     -η Cos[χ]      +κ Cos[ψ] ,
α-β-γ+δ+ζ Cos[τ+ω]-λ Cos[ϕ+ω]-η Cos[χ+ω]+κ Cos[ψ+ω],
α-β-γ+δ+ζ Cos[τ-ω]-λ Cos[ϕ-ω]-η Cos[χ-ω]+κ Cos[ψ-ω]}/12]

sd["Q12"]:=(el=Take[el3,12];rofu={};gi={1,3,2,10,11,12,7,9,8,4,5,6,1,1,1,2,2};
gp={1,1,1,0.,1,0.,1,0.,1,0.,1,0.};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{(((𝕒2𝕓-𝕒2𝕓𝕔+𝕒𝕓-𝕒𝕓𝕔+𝕓-𝕓𝕔))^2)+(((ø+𝕒+𝕒2-𝕒2𝕔-𝕒𝕔-𝕔))^2)}},{{.5 (-(((𝕒2𝕓+𝕒2𝕓𝕔-𝕒𝕓-𝕒𝕓𝕔))^2)+(((-𝕒+𝕒2+𝕒2𝕔-𝕒𝕔))^2)-(((-𝕒2𝕓-𝕒2𝕓𝕔+𝕓+𝕓𝕔))^2)-(((-𝕒𝕓-𝕒𝕓𝕔+𝕓+𝕓𝕔))^2)+(((ø-𝕒2-𝕒2𝕔+𝕔))^2)+(((ø-𝕒-𝕒𝕔+𝕔))^2))}},{{.5 ((((𝕒2𝕓-𝕒2𝕓𝕔-𝕒𝕓+𝕒𝕓𝕔))^2)+(((-𝕒+𝕒2-𝕒2𝕔+𝕒𝕔))^2)+(((-𝕒2𝕓+𝕒2𝕓𝕔+𝕓-𝕓𝕔))^2)+(((-𝕒𝕓+𝕒𝕓𝕔+𝕓-𝕓𝕔))^2)+(((ø-𝕒2+𝕒2𝕔-𝕔))^2)+(((ø-𝕒+𝕒𝕔-𝕔))^2))}}};
sh["Q12"]:=Module[{},gi={1,3,2,10,11,12,7,9,8,4,5,6,1,1,1,2,2};
gp={1,1,1,0.,1,0.,1,0.,1,0.,1,0.};plex=.;
{a+b+c+d+e+f+g+h+i+j+k+l,a+b+c-d-e-f+g+h+i-j-k-l,(((a+b+c-g-h-i))^2)+(((d+e+f-j-k-l))^2),
((((-b+c-h+i))^2)+(((a-c+g-i))^2)+(((a-b+g-h))^2)-(((-e+f-k+l))^2)-(((d-f+j-l))^2)-(((d-e+j-k))^2))/2,
((((-b+c+h-i))^2)+(((a-c-g+i))^2)+(((a-b-g+h))^2)+(((-e+f+k-l))^2)+(((d-f-j+l))^2)+(((d-e-j+k))^2))/2}]);
toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_},"Q12"]:=Module[{ϵ,r=-Sqrt[3],g1=a+b+c-g-h-i,g2=d+e+f-j-k-l,
a1=a-b+g-h,a2=a-b-g+h,
b1=Chop[FullSimplify[b-c+h-i]],b2=Chop[FullSimplify[b-c-h+i]],
c1=-a+c-g+i,c2=-a+c+g-i,
d1=d-e+j-k,d2=d-e-j+k,
e1=Chop[FullSimplify[e-f+k-l]],e2=Chop[FullSimplify[e-f-k+l]],
f1=-d+f-j+l,f2=-d+f+j-l},
Chop[{a+b+c+d+e+f+g+h+i+j+k+l,a+b+c-d-e-f+g+h+i-j-k-l,
ϵ=(g1^2)+(g2^2),If[ϵ==0&&g2==0,0,ArcTan[g1,g2],ArcTan[g1,g2]],
((a1^2)+(b1^2)+(c1^2))/2,If[b1==0,0,ArcTan[a1-c1,r b1]],
((d1^2)+(e1^2)+(f1^2))/2,If[e1==0,0,ArcTan[d1-f1,r e1]],
((a2^2)+(b2^2)+(c2^2))/2,If[b2==0,0,ArcTan[a2-c2,r b2]],
((d2^2)+(e2^2)+(f2^2))/2,If[e2==0,0,ArcTan[d2-f2,r e2]]}]];
toVec[{α_,β_,ϵϵ_,σ_,ζζ_,τ_,λλ_,ϕ_,ηη_,χ_,κκ_,ψ_},"Q12"]:=
Module[{ϵ=2(Sqrt[ϵϵ]),ζ=4(Sqrt[ζζ]),λ=4(Sqrt[λλ]),η=4(Sqrt[ηη]),κ=4(Sqrt[κκ])},{  α+β+ϵ  Cos[σ]+ζ Cos[τ]     +η Cos[χ],
α+β+ϵ  Cos[σ]+ζ Cos[τ+ω]+η Cos[χ+ω], 
α+β+ϵ  Cos[σ]+ζ Cos[τ-ω]+η Cos[χ-ω],
α-β+ϵ  Sin[σ]  +λ Cos[ϕ]        +κ Cos[ψ] ,
α-β+ϵ  Sin[σ]  +λ Cos[ϕ+ω]  +κ Cos[ψ+ω],
α-β+ϵ  Sin[σ]  +λ Cos[ϕ-ω]  +κ Cos[ψ-ω],
α+β-ϵ  Cos[σ]+ζ Cos[τ]     -η Cos[χ]  ,
α+β-ϵ  Cos[σ]+ζ Cos[τ+ω]-η Cos[χ+ω],
α+β-ϵ  Cos[σ]+ζ Cos[τ-ω]-η Cos[χ-ω],
α-β-ϵ  Sin[σ]  +λ Cos[ϕ]        -κ Cos[ψ] ,
α-β-ϵ  Sin[σ]  +λ Cos[ϕ+ω]  -κ Cos[ψ+ω],
α-β-ϵ  Sin[σ]  +λ Cos[ϕ-ω]  -κ Cos[ψ-ω]}/12];

sd["D12"]:=(el=Take[el3,12];rofu={};gi={1,3,2,4,5,6,7,9,8,10,11,12,1,1,1,1,2,2};
gp={1,1,1,1,1,0.,1,0.,1,0.,1,0.};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{ø+𝕒+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔}},{{.5(-(((𝕒2𝕓+𝕒2𝕓𝕔-𝕒𝕓-𝕒𝕓𝕔))^2)+(((𝕒-𝕒2-𝕒2𝕔+𝕒𝕔))^2)-(((𝕒𝕓+𝕒𝕓𝕔-𝕓-𝕓𝕔))^2)-(((-𝕒2𝕓-𝕒2𝕓𝕔+𝕓+𝕓𝕔))^2)+(((-ø+𝕒2+𝕒2𝕔-𝕔))^2)+(((ø-𝕒-𝕒𝕔+𝕔))^2))}},{{.5 (-(((𝕒2𝕓-𝕒2𝕓𝕔-𝕒𝕓+𝕒𝕓𝕔))^2)+(((𝕒-𝕒2+𝕒2𝕔-𝕒𝕔))^2)-(((-𝕒2𝕓+𝕒2𝕓𝕔+𝕓-𝕓𝕔))^2)-(((𝕒𝕓-𝕒𝕓𝕔-𝕓+𝕓𝕔))^2)+(((ø-𝕒+𝕒𝕔-𝕔))^2)+(((-ø+𝕒2-𝕒2𝕔+𝕔))^2))}}});
toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_},"D12"]:=Module[{r=-Sqrt[3],a1=a-b+g-h,a2=-d+e-j+k,a3=a-b-g+h,a4=-d+e+j-k,
b1=Chop[FullSimplify[b-c+h-i]],b2=Chop[FullSimplify[-e+f-k+l]],
b3=Chop[FullSimplify[b-c-h+i]],b4=Chop[FullSimplify[-e+f+k-l]],
c1=-a+c-g+i,c2=d-f+j-l,c3=-a+c+g-i,c4=d-f-j+l},
Chop[{a+b+c+d+e+f+g+h+i+j+k+l,a+b+c-d-e-f+g+h+i-j-k-l,
a+b+c+d+e+f-g-h-i-j-k-l,a+b+c-d-e-f-g-h-i+j+k+l,
((a1^2)+(b1^2)+(c1^2))/2,If[b1==0,0,ArcTan[a1-c1,r b1]],
((a2^2)+(b2^2)+(c2^2))/2,If[b2==0,0,ArcTan[a2-c2,r b2]],
((a3^2)+(b3^2)+(c3^2))/2,If[b3==0,0,ArcTan[a3-c3,r b3]],
((a4^2)+(b4^2)+(c4^2))/2,If[b4==0,0,ArcTan[a4-c4,r b4]]}]];
toVec[{α_,β_,γ_,δ_,ζζ_,τ_,λλ_,ϕ_,ηη_,χ_,κκ_,ψ_},"D12"]:=
Module[{ζ=4(Sqrt[ζζ]),λ=4(Sqrt[λλ]),η=4(Sqrt[ηη]),κ=4(Sqrt[κκ])},{      
α+β+γ+δ+ζ Cos[τ]      +η Cos[χ],
α+β+γ+δ+ζ Cos[τ+ω]+η Cos[χ+ω], 
α+β+γ+δ+ζ Cos[τ-ω]+η Cos[χ-ω],
α-β+γ-δ-λ Cos[ϕ]      -κ Cos[ψ] ,
α-β+γ-δ-λ Cos[ϕ+ω]-κ Cos[ψ+ω],
α-β+γ-δ-λ Cos[ϕ-ω]-κ Cos[ψ-ω],
α+β-γ-δ+ζ Cos[τ]      -η Cos[χ] ,
α+β-γ-δ+ζ Cos[τ+ω]-η Cos[χ+ω],
α+β-γ-δ+ζ Cos[τ-ω]-η Cos[χ-ω],
α-β-γ+δ-λ Cos[ϕ]      +κ Cos[ψ] ,
α-β-γ+δ-λ Cos[ϕ+ω]+κ Cos[ψ+ω],
α-β-γ+δ-λ Cos[ϕ-ω]+κ Cos[ψ-ω]}/12];

sd["A4"]:=(gp=.;el=Take[el3,12];rofu={};gi={1,3,2,4,9,11,7,12,5,10,6,8,1,1,3};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔))^2)+(((-ø+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔-𝕓-𝕓𝕔-𝕔))^2)+(((ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2))/2}},{{ø-𝕓+𝕓𝕔-𝕔,-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔,-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔},{-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔,ø+𝕓-𝕓𝕔-𝕔,𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔},{-𝕒2+𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔,𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔,ø-𝕓-𝕓𝕔+𝕔}}});

sd["CL021"]:=(
el=Take[el3,12];rofu={};gi={1,-2,-3,-4,9,-10,-11,-12,5,-6,-7,-8,2,2};gp={};
sh={{{(((ø+𝕒2𝕔+𝕒𝕓))^2)+(((𝕒2𝕓𝕔+𝕒𝕔+𝕓))^2)+(((𝕒+𝕒2𝕓+𝕓𝕔))^2)+(((𝕒2+𝕒𝕓𝕔+𝕔))^2)}},{{((((((𝕒-𝕒2𝕓))^2)+(((-ø+𝕒2𝕔))^2)+(((ø-𝕒𝕓))^2)+(((-𝕒2𝕔+𝕒𝕓))^2)+(((-𝕒2+𝕒𝕓𝕔))^2)+(((-𝕒2𝕓𝕔+𝕒𝕔))^2)+(((𝕒2𝕓𝕔-𝕓))^2)+(((-𝕒𝕔+𝕓))^2)+(((𝕒2𝕓-𝕓𝕔))^2)+(((-𝕒+𝕓𝕔))^2)+(((𝕒2-𝕔))^2)+(((-𝕒𝕓𝕔+𝕔))^2)))^2)/4-3 ((((ø 𝕒2𝕓𝕔-𝕒2𝕓𝕔 𝕒𝕓-ø 𝕒𝕔+𝕒2𝕔 𝕒𝕔-𝕒2𝕔 𝕓+𝕒𝕓 𝕓))^2)+(((-ø 𝕒2𝕓-𝕒 𝕒2𝕔+𝕒2𝕓 𝕒2𝕔+𝕒 𝕒𝕓+ø 𝕓𝕔-𝕒𝕓 𝕓𝕔))^2)+(((-𝕒 𝕒2𝕓𝕔+𝕒2𝕓 𝕒2𝕓𝕔+𝕒 𝕒𝕔-𝕒2𝕓 𝕓-𝕒𝕔 𝕓𝕔+𝕓 𝕓𝕔))^2)+(((-𝕒2 𝕒2𝕔+𝕒2 𝕒𝕓+ø 𝕒𝕓𝕔-𝕒𝕓 𝕒𝕓𝕔-ø 𝕔+𝕒2𝕔 𝕔))^2)+(((𝕒2 𝕒2𝕓𝕔-𝕒2 𝕒𝕔+𝕒𝕓𝕔 𝕒𝕔-𝕒𝕓𝕔 𝕓-𝕒2𝕓𝕔 𝕔+𝕓 𝕔))^2)+(((𝕒2 𝕒2𝕓+𝕒 𝕒𝕓𝕔-𝕒2𝕓 𝕒𝕓𝕔-𝕒2 𝕓𝕔-𝕒 𝕔+𝕓𝕔 𝕔))^2))}}});

sd["C3P4"]:=(el=Take[el3,12];rofu={};gi={1,3,2,4,6,5,7,9,8,10,12,11,2,2};gp={};
sh={{{(((ø+𝕒+𝕒2))^2)-(((𝕒2𝕓+𝕒𝕓+𝕓))^2)-(((𝕒2𝕓𝕔+𝕒𝕓𝕔+𝕓𝕔))^2)-(((𝕒2𝕔+𝕒𝕔+𝕔))^2)}},{{((((((ø-𝕒))^2)+(((ø-𝕒2))^2)+(((𝕒-𝕒2))^2)-(((-𝕒2𝕓+𝕒𝕓))^2)-(((-𝕒2𝕓𝕔+𝕒𝕓𝕔))^2)-(((-𝕒2𝕔+𝕒𝕔))^2)-(((-𝕒2𝕓+𝕓))^2)-(((-𝕒𝕓+𝕓))^2)-(((-𝕒2𝕓𝕔+𝕓𝕔))^2)-(((-𝕒𝕓𝕔+𝕓𝕔))^2)-(((-𝕒2𝕔+𝕔))^2)-(((-𝕒𝕔+𝕔))^2)))^2)/4+3 ((((ø 𝕒2𝕓-𝕒 𝕒2𝕓-ø 𝕒𝕓+𝕒2 𝕒𝕓+𝕒 𝕓-𝕒2 𝕓))^2)+(((ø 𝕒2𝕓𝕔-𝕒 𝕒2𝕓𝕔-ø 𝕒𝕓𝕔+𝕒2 𝕒𝕓𝕔+𝕒 𝕓𝕔-𝕒2 𝕓𝕔))^2)-(((𝕒2𝕓𝕔 𝕒𝕓-𝕒2𝕓 𝕒𝕓𝕔-𝕒2𝕓𝕔 𝕓+𝕒𝕓𝕔 𝕓+𝕒2𝕓 𝕓𝕔-𝕒𝕓 𝕓𝕔))^2)+(((ø 𝕒2𝕔-𝕒 𝕒2𝕔-ø 𝕒𝕔+𝕒2 𝕒𝕔+𝕒 𝕔-𝕒2 𝕔))^2)-(((-𝕒2𝕔 𝕒𝕓+𝕒2𝕓 𝕒𝕔+𝕒2𝕔 𝕓-𝕒𝕔 𝕓-𝕒2𝕓 𝕔+𝕒𝕓 𝕔))^2)-(((𝕒2𝕔 𝕒𝕓𝕔-𝕒2𝕓𝕔 𝕒𝕔-𝕒2𝕔 𝕓𝕔+𝕒𝕔 𝕓𝕔+𝕒2𝕓𝕔 𝕔-𝕒𝕓𝕔 𝕔))^2))}}});

sd["C6Kr"]:=(el=Take[el3,12];rofu={};gi={1,3,2,4,6,5,7,9,8,10,12,11,1,1,1,1,1,1,1,1};
gp={1,1,1,1,1,0.,1,0.,1,0.,1,0.};
sh={{{ø-𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔}},{{ø-𝕒-𝕒2+𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓𝕔-𝕔}},{{ø-𝕒-𝕒2+𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔}},{{ø-𝕒-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔-𝕔}},{{.5 ((((𝕒-𝕒2+𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔))^2)+(((ø+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕓+𝕓𝕔-𝕔))^2)+(((ø+𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔))^2))}},{{.5 ((((𝕒-𝕒2+𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕓-𝕓𝕔+𝕔))^2)+(((ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔))^2))}},{{.5 ((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕓+𝕓𝕔+𝕔))^2)+(((ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2))}},{{.5((((𝕒-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔))^2)+(((ø+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕓-𝕓𝕔-𝕔))^2)+(((ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔))^2))}}});

sd["C3KC2r"]:=(el=Take[el3,12];rofu={};gi={1,3,2,4,6,5,7,9,8,10,12,11,1,1,1,1,1,1,1,1};
gp={1,1,1,1,1,0.,1,0.,1,0.,1,0.};
sh={{{ø+𝕒+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔-𝕔}},{{ø+𝕒+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔-𝕔}},{{.5 ((((𝕒-𝕒2-𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔-𝕔))^2)+(((-ø+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔-𝕓-𝕓𝕔+𝕔))^2))}},{{ .5((((𝕒-𝕒2+𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔))^2)+(((-ø+𝕒2-𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔+𝕓-𝕓𝕔-𝕔))^2)+(((ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓𝕔+𝕔))^2))}},
{{.5((((𝕒-𝕒2+𝕒2𝕓+𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔))^2)+(((ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔-𝕔))^2)+(((-ø+𝕒2-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔+𝕓+𝕓𝕔+𝕔))^2))}},{{.5 ((((𝕒-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔))^2)+(((-ø+𝕒2+𝕒2𝕓-𝕒2𝕓𝕔-𝕒2𝕔-𝕓+𝕓𝕔-𝕔))^2)+(((ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔+𝕔))^2))}}});

9.11 Polar-Vector, Hyperbolics, sh, toPol, toVec, tohyPol, tohyVec for 16 element loops.

sd["D16"]=(el=Take[el2,16];rofu={};gi={1,2,15,4,13,6,11,8,9,10,7,12,5,14,3,16,1,1,1,1,2,2};gp={};sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{-(((𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕))^2)-(((𝕒-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕))^2)+(((ø-𝕔-𝕔𝕕+𝕕))^2)}},{{-2(((-(𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕔-𝕒𝕔𝕕)-(𝕒𝕓-𝕒𝕓𝕕) (𝕒𝕔-𝕒𝕔𝕕)+(𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒-𝕒𝕕)-(𝕒𝕓-𝕒𝕓𝕕) (𝕒-𝕒𝕕)+(𝕓𝕔-𝕓𝕔𝕕) (𝕔-𝕔𝕕)+(𝕓-𝕓𝕕) (𝕔-𝕔𝕕)-(𝕓𝕔-𝕓𝕔𝕕) (ø-𝕕)+(𝕓-𝕓𝕕) (ø-𝕕)))^2)+(((-(((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2)-(((𝕒𝕓-𝕒𝕓𝕕))^2)-(((𝕒𝕔-𝕒𝕔𝕕))^2)-(((𝕒-𝕒𝕕))^2)+(((𝕓𝕔-𝕓𝕔𝕕))^2)+(((𝕓-𝕓𝕕))^2)+(((𝕔-𝕔𝕕))^2)+(((ø-𝕕))^2)))^2)}}});

sd["Q16"]:=(el=Take[el2,16];rofu={};gi={1,10,15,12,13,14,11,16,9,2,7,4,5,6,3,8,1,1,1,1,2,2};gp={};sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{-(((𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕))^2)-(((𝕒-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕))^2)+(((ø-𝕔-𝕔𝕕+𝕕))^2),(((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^4)+2 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (((𝕒𝕓-𝕒𝕓𝕕))^2)+(((𝕒𝕓-𝕒𝕓𝕕))^4)-4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕓-𝕒𝕓𝕕) (((𝕒𝕔-𝕒𝕔𝕕))^2)+(((𝕒𝕔-𝕒𝕔𝕕))^4)+4 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (𝕒𝕔-𝕒𝕔𝕕) (𝕒-𝕒𝕕)-4 (((𝕒𝕓-𝕒𝕓𝕕))^2) (𝕒𝕔-𝕒𝕔𝕕) (𝕒-𝕒𝕕)+4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕓-𝕒𝕓𝕕) (((𝕒-𝕒𝕕))^2)+2 (((𝕒𝕔-𝕒𝕔𝕕))^2) (((𝕒-𝕒𝕕))^2)+(((𝕒-𝕒𝕕))^4)+2 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (((𝕓𝕔-𝕓𝕔𝕕))^2)+2 (((𝕒𝕓-𝕒𝕓𝕕))^2) (((𝕓𝕔-𝕓𝕔𝕕))^2)+2 (((𝕒𝕔-𝕒𝕔𝕕))^2) (((𝕓𝕔-𝕓𝕔𝕕))^2)+2 (((𝕒-𝕒𝕕))^2) (((𝕓𝕔-𝕓𝕔𝕕))^2)+(((𝕓𝕔-𝕓𝕔𝕕))^4)+2 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (((𝕓-𝕓𝕕))^2)+2 (((𝕒𝕓-𝕒𝕓𝕕))^2) (((𝕓-𝕓𝕕))^2)+2 (((𝕒𝕔-𝕒𝕔𝕕))^2) (((𝕓-𝕓𝕕))^2)+2 (((𝕒-𝕒𝕕))^2) (((𝕓-𝕓𝕕))^2)+2 (((𝕓𝕔-𝕓𝕔𝕕))^2) (((𝕓-𝕓𝕕))^2)+(((𝕓-𝕓𝕕))^4)-4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓𝕔-𝕓𝕔𝕕) (𝕔-𝕔𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓𝕔-𝕓𝕔𝕕) (𝕔-𝕔𝕕)+4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒-𝕒𝕕) (𝕓𝕔-𝕓𝕔𝕕) (𝕔-𝕔𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒-𝕒𝕕) (𝕓𝕔-𝕓𝕔𝕕) (𝕔-𝕔𝕕)-4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓-𝕓𝕕) (𝕔-𝕔𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓-𝕓𝕕) (𝕔-𝕔𝕕)+4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒-𝕒𝕕) (𝕓-𝕓𝕕) (𝕔-𝕔𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒-𝕒𝕕) (𝕓-𝕓𝕕) (𝕔-𝕔𝕕)+2 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (((𝕔-𝕔𝕕))^2)+2 (((𝕒𝕓-𝕒𝕓𝕕))^2) (((𝕔-𝕔𝕕))^2)+2 (((𝕒𝕔-𝕒𝕔𝕕))^2) (((𝕔-𝕔𝕕))^2)+2 (((𝕒-𝕒𝕕))^2) (((𝕔-𝕔𝕕))^2)-4 (𝕓𝕔-𝕓𝕔𝕕) (𝕓-𝕓𝕕) (((𝕔-𝕔𝕕))^2)+(((𝕔-𝕔𝕕))^4)+4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓𝕔-𝕓𝕔𝕕) (ø-𝕕)+4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓𝕔-𝕓𝕔𝕕) (ø-𝕕)-4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒-𝕒𝕕) (𝕓𝕔-𝕓𝕔𝕕) (ø-𝕕)+4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒-𝕒𝕕) (𝕓𝕔-𝕓𝕔𝕕) (ø-𝕕)-4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓-𝕓𝕕) (ø-𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒𝕔-𝕒𝕔𝕕) (𝕓-𝕓𝕕) (ø-𝕕)+4 (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕) (𝕒-𝕒𝕕) (𝕓-𝕓𝕕) (ø-𝕕)-4 (𝕒𝕓-𝕒𝕓𝕕) (𝕒-𝕒𝕕) (𝕓-𝕓𝕕) (ø-𝕕)+4 (((𝕓𝕔-𝕓𝕔𝕕))^2) (𝕔-𝕔𝕕) (ø-𝕕)-4 (((𝕓-𝕓𝕕))^2) (𝕔-𝕔𝕕) (ø-𝕕)+2 (((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2) (((ø-𝕕))^2)+2 (((𝕒𝕓-𝕒𝕓𝕕))^2) (((ø-𝕕))^2)+2 (((𝕒𝕔-𝕒𝕔𝕕))^2) (((ø-𝕕))^2)+2 (((𝕒-𝕒𝕕))^2) (((ø-𝕕))^2)+4 (𝕓𝕔-𝕓𝕔𝕕) (𝕓-𝕓𝕕) (((ø-𝕕))^2)+2 (((𝕔-𝕔𝕕))^2) (((ø-𝕕))^2)+(((ø-𝕕))^4)}}});sd["C2D8"]:=(el=Take[el2,16];rofu={};gi={1,2,7,4,5,6,3,8,9,10,15,12,13,14,11,16,1,1,1,1,1,1,1,1,2,2};gp=.;sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{-(((𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕))^2)-(((𝕒-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕))^2)+(((ø-𝕔-𝕔𝕕+𝕕))^2),-(((𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕))^2)-(((𝕒-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕))^2)+(((𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕))^2)+(((ø-𝕔+𝕔𝕕-𝕕))^2)}}});

sd["C4C4"]:=(el=Take[el2,16];rofu={};gi={1,4,3,2,13,16,15,14,9,12,11,10,5,8,7,6,1,1,1,1,1,1,1,1,1,1};gp=.;
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{(((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕔-𝕒𝕔𝕕+𝕓𝕔-𝕓𝕔𝕕+𝕔-𝕔𝕕))^2)+(((ø+𝕒+𝕒𝕓-𝕒𝕓𝕕-𝕒𝕕+𝕓-𝕓𝕕-𝕕))^2)}},{{(((-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕓𝕔-𝕓𝕔𝕕+𝕔-𝕔𝕕))^2)+(((ø-𝕒-𝕒𝕓+𝕒𝕓𝕕+𝕒𝕕+𝕓-𝕓𝕕-𝕕))^2)}},{{(((𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕))^2)}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕))^2)}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕕-𝕒𝕕+𝕓𝕔-𝕓𝕔𝕕-𝕔+𝕔𝕕))^2)+(((ø-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕓+𝕓𝕕-𝕕))^2)}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕕-𝕒𝕕-𝕓𝕔+𝕓𝕔𝕕+𝕔-𝕔𝕕))^2)+(((ø+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕓+𝕓𝕕-𝕕))^2)}}});

(*sd["P16"]:=(el=Take[el2,16];rofu={};gi={1,6,7,8,5,2,3,4,9,14,15,16,13,10,11,12,1,1,1,1,1,1,1,1,2,2};gp=.;
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{(((𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕))^2)+(((𝕒-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕))^2)+(((ø-𝕔-𝕔𝕕+𝕕))^2),(((𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕))^2)+(((𝕒-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕))^2)+𝕓-(((𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕))^2)+(((ø-𝕔+𝕔𝕕-𝕕))^2)}}});*)

sd["C2C2C2C2"]:=(el=Take[el2,16];rofu={};gi={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
gp={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕-𝕓+𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔+𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕-𝕓+𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔+𝕔𝕕-𝕕}}});toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_,m_,n_,o_,p_},"C2C2C2C2"]:={a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p,a-b-c+d+e-f-g+h+i-j-k+l+m-n-o+p,a-b+c-d+e-f+g-h+i-j+k-l+m-n+o-p,a+b-c-d+e+f-g-h+i+j-k-l+m+n-o-p,a-b+c-d-e+f-g+h+i-j+k-l-m+n-o+p,a+b-c-d-e-f+g+h+i+j-k-l-m-n+o+p,a+b+c+d-e-f-g-h+i+j+k+l-m-n-o-p,a-b-c+d-e+f+g-h+i-j-k+l-m+n+o-p,a+b+c+d+e+f+g+h-i-j-k-l-m-n-o-p,a+b+c+d-e-f-g-h-i-j-k-l+m+n+o+p,a+b-c-d-e-f+g+h-i-j+k+l+m+n-o-p,a-b+c-d-e+f-g+h-i+j-k+l+m-n+o-p,a+b-c-d+e+f-g-h-i-j+k+l-m-n+o+p,a-b-c+d+e-f-g+h-i+j+k-l-m+n+o-p,a-b+c-d+e-f+g-h-i+j-k+l-m+n-o+p,a-b-c+d-e+f+g-h-i+j+k-l+m-n-o+p};toVec[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_,m_,n_,o_,p_},"C2C2C2C2"]:={a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p,a-b-c+d-e+f+g-h+i+j+k-l+m-n-o-p,a-b+c-d+e-f+g-h+i+j-k+l-m-n+o-p,a+b-c-d-e-f+g+h+i+j-k-l-m+n-o+p,a+b+c+d-e-f-g-h+i-j-k-l+m+n+o-p,a-b-c+d+e-f-g+h+i-j-k+l+m-n-o+p,a-b+c-d-e+f-g+h+i-j+k-l-m-n+o+p,a+b-c-d+e+f-g-h+i-j+k+l-m+n-o-p,a+b+c+d+e+f+g+h-i-j-k-l-m-n-o-p,a-b-c+d-e+f+g-h-i-j-k+l-m+n+o+p,a-b+c-d+e-f+g-h-i-j+k-l+m+n-o+p,a+b-c-d-e-f+g+h-i-j+k+l+m-n+o-p,a+b+c+d-e-f-g-h-i+j+k+l-m-n-o+p,a-b-c+d+e-f-g+h-i+j+k-l-m+n+o-p,a-b+c-d-e+f-g+h-i+j-k+l+m+n-o-p,a+b-c-d+e+f-g-h-i+j-k-l+m-n+o+p}/16;

sd["C4C2C2"]:=(el=Take[el2,16];rofu={};gi={1,4,3,2,5,8,7,6,9,12,11,10,13,16,15,14,1,1,1,1,1,1,1,1,1,1,1,1};gp={1,1,1,1,1,1,1,1,1,0.,1,0.,1,0.,1,0.};
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕))^2)+(((ø-𝕓+𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔+𝕔𝕕-𝕕))^2)}},{{(((𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕))^2)+(((ø-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕))^2)}},{{(((𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕))^2)}},{{(((𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕))^2)}}});toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_,m_,n_,o_,p_},"C4C2C2"]:=
{a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p,a+b+c+d-e-f-g-h-i-j-k-l+m+n+o+p,a-b+c-d+e-f+g-h-i+j-k+l-m+n-o+p,
a-b+c-d-e+f-g+h+i-j+k-l-m+n-o+p,
a-b+c-d-e+f-g+h-i+j-k+l+m-n+o-p,
a-b+c-d+e-f+g-h+i-j+k-l+m-n+o-p,
a+b+c+d-e-f-g-h+i+j+k+l-m-n-o-p,
a+b+c+d+e+f+g+h-i-j-k-l-m-n-o-p,
(*ij*)(((a-c-e+g-i+k+m-o))^2)+(((b-d-f+h-j+l+n-p))^2),If[b-d-f+h-j+l+n-p==0,0,ArcTan[a-c-e+g-i+k+m-o,b-d-f+h-j+l+n-p]],
(*kl*)(((a-c+e-g-i+k-m+o))^2)+(((b-d+f-h-j+l-n+p))^2),If[b-d+f-h-j+l-n+p==0,0,ArcTan[a-c+e-g-i+k-m+o,b-d+f-h-j+l-n+p]],
(*mn*)(((a-c-e+g+i-k-m+o))^2)+(((b-d-f+h+j-l-n+p))^2),If[b-d-f+h+j-l-n+p==0,0,ArcTan[a-c-e+g+i-k-m+o,b-d-f+h+j-l-n+p]],
(*op*)(((a-c+e-g+i-k+m-o))^2)+(((b-d+f-h+j-l+n-p))^2),If[b-d+f-h+j-l+n-p==0,0,ArcTan[a-c+e-g+i-k+m-o,b-d+f-h+j-l+n-p]]};toVec[{a_,b_,c_,d_,e_,f_,g_,h_,ii_,j_,kk_,l_,mm_,n_,oo_,p_},
"C4C2C2"]:=Module[{i=2(Sqrt[ii]),k=2(Sqrt[kk]),m=2(Sqrt[mm]),o=2(Sqrt[oo])},
{  (*a*)a+b+c+d+e+f+g+h+i Cos[j]+k Cos[l]+m Cos[n]+o Cos[p],
(*b*)a+b-c-d-e-f+g+h+i Sin[j]+k Sin[l]+m Sin[n]+o Sin[p],
(*c*)a+b+c+d+e+f+g+h-i Cos[j]-k Cos[l]-m Cos[n]-o Cos[p],
(*d*)a+b-c-d-e-f+g+h-i Sin[j]-k Sin[l]-m Sin[n]-o Sin[p],
(*e*)a-b+c-d-e+f-g+h-i Cos[j]+k Cos[l]-m Cos[n]+o Cos[p],
(*f*)a-b-c+d+e-f-g+h-i Sin[j]+k Sin[l]-m Sin[n]+o Sin[p],
(*g*)a-b+c-d-e+f-g+h+i Cos[j]-k Cos[l]+m Cos[n]-o Cos[p],
(*h*)a-b-c+d+e-f-g+h+i Sin[j]-k Sin[l]+m Sin[n]-o Sin[p],
(*i*)a-b-c+d-e+f+g-h-i Cos[j]-k Cos[l]+m Cos[n]+o Cos[p],
(*j*)a-b+c-d+e-f+g-h-i Sin[j]-k Sin[l]+m Sin[n]+o Sin[p],
(*k*)a-b-c+d-e+f+g-h+i Cos[j]+k Cos[l]-m Cos[n]-o Cos[p],
(*l*)a-b+c-d+e-f+g-h+i Sin[j]+k Sin[l]-m Sin[n]-o Sin[p],
(*m*)a+b-c-d+e+f-g-h+i Cos[j]-k Cos[l]-m Cos[n]+o Cos[p],
(*n*)a+b+c+d-e-f-g-h+i Sin[j]-k Sin[l]-m Sin[n]+o Sin[p],
(*o*)a+b-c-d+e+f-g-h-i Cos[j]+k Cos[l]+m Cos[n]-o Cos[p],
(*p*)a+b+c+d-e-f-g-h-i Sin[j]+k Sin[l]+m Sin[n]-o Sin[p]}/16];

sd["C2C2iC4"]:=(el=Take[el2,16];rofu={};gi={1,2,3,4,13,16,15,14,9,10,11,12,5,8,7,6,1,1,1,1,1,1,1,1,2,2,2,2};gp=.;
sh={ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕,ø+𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕,ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕,ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕,ø-𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔+𝕔𝕕-𝕕,ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕,ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕,ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕,(((𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕))^2)+(((ø-𝕓+𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔+𝕔𝕕-𝕕))^2),(((𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕))^2)+(((ø-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕))^2),(((𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕))^2),(((𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕))^2)+(((ø-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕))^2)});
sd["C4iC4"]:=(el=Take[el2,16];rofu={};gp=.;gi={1,4,3,2,13,14,15,16,9,12,11,10,5,6,7,8,1,1,1,1,1,1,2,2};
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{(((-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕔+𝕒𝕔𝕕-𝕓𝕔+𝕓𝕔𝕕-𝕔+𝕔𝕕))^2)+(((ø+𝕒+𝕒𝕓-𝕒𝕓𝕕-𝕒𝕕+𝕓-𝕓𝕕-𝕕))^2)}},{{(((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕓𝕔+𝕓𝕔𝕕-𝕔+𝕔𝕕))^2)+(((ø-𝕒-𝕒𝕓+𝕒𝕓𝕕+𝕒𝕕+𝕓-𝕓𝕕-𝕕))^2)}},{{-(((-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕔+𝕒𝕔𝕕))^2)+(((𝕒-𝕒𝕓-𝕒𝕓𝕕+𝕒𝕕))^2)-(((-𝕓𝕔-𝕓𝕔𝕕+𝕔+𝕔𝕕))^2)+(((ø-𝕓-𝕓𝕕+𝕕))^2),(((-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕔-𝕒𝕔𝕕))^2)+(((𝕒-𝕒𝕓+𝕒𝕓𝕕-𝕒𝕕))^2)+(((-𝕓𝕔+𝕓𝕔𝕕+𝕔-𝕔𝕕))^2)+(((ø-𝕓+𝕓𝕕-𝕕))^2)}}});

sd["QD16"]:=(el=Take[el2,16];rofu={};gi={1,2,3,4,13,14,15,16,9,10,11,12,5,6,7,8,1,1,1,1,1,1,1,1,2,2};gp=.;
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{-(((𝕒𝕓+I (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕)-𝕒𝕓𝕕))^2)-(((𝕒+I (𝕒𝕔-𝕒𝕔𝕕)-𝕒𝕕))^2)-(((𝕓+I (𝕓𝕔-𝕓𝕔𝕕)-𝕓𝕕))^2)+(((ø+I (𝕔-𝕔𝕕)-𝕕))^2)}},{{-(((𝕒𝕓-I (𝕒𝕓𝕔-𝕒𝕓𝕔𝕕)-𝕒𝕓𝕕))^2)-(((𝕒-I (𝕒𝕔-𝕒𝕔𝕕)-𝕒𝕕))^2)-(((𝕓-I (𝕓𝕔-𝕓𝕔𝕕)-𝕓𝕕))^2)+(((ø-I (𝕔-𝕔𝕕)-𝕕))^2)}}});sd["Oct"]:=(el=Take[el2,16];rofu={};gi={1,10,11,12,13,14,15,16,9,2,3,4,5,6,7,8,1,1,1,1,1,1,1,1,4};gp=.;
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕+𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕-𝕓+𝕓𝕔+𝕓𝕔𝕕-𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{(((𝕒𝕓𝕔-𝕒𝕓𝕔𝕕))^2)+(((𝕒𝕓-𝕒𝕓𝕕))^2)+(((𝕒𝕔-𝕒𝕔𝕕))^2)+(((𝕒-𝕒𝕕))^2)+(((𝕓𝕔-𝕓𝕔𝕕))^2)+(((𝕓-𝕓𝕕))^2)+(((𝕔-𝕔𝕕))^2)+(((ø-𝕕))^2)}}});

sd["Q8M"]:=(el=Take[el2,16];rofu={};gi={1,6,7,8,5,2,3,4,9,10,11,12,13,14,
15,16,1,1,1,1,1,1,1,1,4};gp=.;
sh={{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø-𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔-𝕓𝕔𝕕-𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓-𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔-𝕔𝕕-𝕕}},{{ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{(((𝕒𝕓-𝕒𝕓𝕔))^2)-(((𝕒𝕓𝕔𝕕-𝕒𝕓𝕕))^2)+(((𝕒-𝕒𝕔))^2)-(((𝕒𝕔𝕕-𝕒𝕕))^2)+(((𝕓-𝕓𝕔))^2)-(((𝕓𝕔𝕕-𝕓𝕕))^2)+(((ø-𝕔))^2)-(((𝕔𝕕-𝕕))^2)}}});

sd["CL13"]:=(el=Take[el2,16];rofu={};gi={1,2,-3,4,-5,6,-7,-8,-9,10,-11,-12,-13,-14,15,-16,4};gp=.;sh={{{((((ø^2)+(𝕒^2)+((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕓𝕔𝕕)^2)+((𝕒𝕓𝕕)^2)+((𝕒𝕔)^2)+((𝕒𝕔𝕕)^2)+((𝕒𝕕)^2)+(𝕓^2)+((𝕓𝕔)^2)+((𝕓𝕔𝕕)^2)+((𝕓𝕕)^2)+(𝕔^2)+((𝕔𝕕)^2)+(𝕕^2)))^2)+4 (-(((ø 𝕒𝕕-𝕒𝕓𝕕 𝕓+𝕒𝕓𝕔𝕕 𝕓𝕔-𝕒𝕓𝕔 𝕓𝕔𝕕+𝕒𝕓 𝕓𝕕-𝕒𝕔𝕕 𝕔+𝕒𝕔 𝕔𝕕-𝕒 𝕕))^2)-(((ø 𝕒𝕓-𝕒 𝕓-𝕒𝕔 𝕓𝕔-𝕒𝕔𝕕 𝕓𝕔𝕕-𝕒𝕕 𝕓𝕕+𝕒𝕓𝕔 𝕔+𝕒𝕓𝕔𝕕 𝕔𝕕+𝕒𝕓𝕕 𝕕))^2)-(((ø 𝕒𝕔-𝕒𝕓𝕔 𝕓+𝕒𝕓 𝕓𝕔+𝕒𝕓𝕕 𝕓𝕔𝕕-𝕒𝕓𝕔𝕕 𝕓𝕕-𝕒 𝕔-𝕒𝕕 𝕔𝕕+𝕒𝕔𝕕 𝕕))^2)-(((ø 𝕒+𝕒𝕓 𝕓+𝕒𝕓𝕔 𝕓𝕔+𝕒𝕓𝕔𝕕 𝕓𝕔𝕕+𝕒𝕓𝕕 𝕓𝕕+𝕒𝕔 𝕔+𝕒𝕔𝕕 𝕔𝕕+𝕒𝕕 𝕕))^2)-(((-𝕒 𝕒𝕓𝕔𝕕-𝕒𝕓𝕕 𝕒𝕔+𝕒𝕓 𝕒𝕔𝕕+𝕒𝕓𝕔 𝕒𝕕+ø 𝕓𝕔𝕕+𝕓𝕕 𝕔-𝕓 𝕔𝕕-𝕓𝕔 𝕕))^2))}}});
sd["CL22"]:=(el=Take[el2,16];rofu={};gi={1,2,3,-4,-5,6,7,8,-9,10,11,12,-13,-14,-15,16,4};gp=.;sh={{{((((ø^2)+(𝕒^2)+((𝕒𝕓)^2)-((𝕒𝕓𝕔)^2)+((𝕒𝕓𝕔𝕕)^2)-((𝕒𝕓𝕕)^2)-((𝕒𝕔)^2)+((𝕒𝕔𝕕)^2)-((𝕒𝕕)^2)+(𝕓^2)-((𝕓𝕔)^2)+((𝕓𝕔𝕕)^2)-((𝕓𝕕)^2)-(𝕔^2)+((𝕔𝕕)^2)-(𝕕^2)))^2)+4 ((((𝕒𝕓𝕔 𝕒𝕓𝕔𝕕+𝕒𝕓 𝕒𝕓𝕕-𝕒𝕔 𝕒𝕔𝕕-𝕒 𝕒𝕕-𝕓𝕔 𝕓𝕔𝕕-𝕓 𝕓𝕕+𝕔 𝕔𝕕+ø 𝕕))^2)-(((ø 𝕒𝕓𝕔𝕕+𝕒𝕔𝕕 𝕓-𝕒𝕕 𝕓𝕔-𝕒 𝕓𝕔𝕕+𝕒𝕔 𝕓𝕕-𝕒𝕓𝕕 𝕔-𝕒𝕓 𝕔𝕕+𝕒𝕓𝕔 𝕕))^2)-(((ø 𝕒+𝕒𝕓 𝕓-𝕒𝕓𝕔 𝕓𝕔+𝕒𝕓𝕔𝕕 𝕓𝕔𝕕-𝕒𝕓𝕕 𝕓𝕕-𝕒𝕔 𝕔+𝕒𝕔𝕕 𝕔𝕕-𝕒𝕕 𝕕))^2)-(((-𝕒 𝕒𝕓+𝕒𝕓𝕔 𝕒𝕔-𝕒𝕓𝕔𝕕 𝕒𝕔𝕕+𝕒𝕓𝕕 𝕒𝕕+ø 𝕓-𝕓𝕔 𝕔+𝕓𝕔𝕕 𝕔𝕕-𝕓𝕕 𝕕))^2)+(((𝕒𝕓 𝕒𝕓𝕔-𝕒𝕓𝕔𝕕 𝕒𝕓𝕕-𝕒 𝕒𝕔+𝕒𝕔𝕕 𝕒𝕕-𝕓 𝕓𝕔+𝕓𝕔𝕕 𝕓𝕕+ø 𝕔-𝕔𝕕 𝕕))^2))}}});

sd["CL31"]:=(el=Take[el2,16];rofu={};gi={1,2,3,-4,5,-6,-7,-8,-9,10,11,12,13,14,15,-16,4};gp=.;sh={{{((((ø^2)+(𝕒^2)-((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕓𝕔𝕕)^2)-((𝕒𝕓𝕕)^2)-((𝕒𝕔)^2)-((𝕒𝕔𝕕)^2)+((𝕒𝕕)^2)-(𝕓^2)+((𝕓𝕔)^2)+((𝕓𝕔𝕕)^2)-((𝕓𝕕)^2)-(𝕔^2)-((𝕔𝕕)^2)+(𝕕^2)))^2)+4 (-(((ø 𝕒𝕕+𝕒𝕓𝕕 𝕓+𝕒𝕓𝕔𝕕 𝕓𝕔-𝕒𝕓𝕔 𝕓𝕔𝕕-𝕒𝕓 𝕓𝕕+𝕒𝕔𝕕 𝕔-𝕒𝕔 𝕔𝕕-𝕒 𝕕))^2)+(((ø 𝕒𝕓-𝕒 𝕓+𝕒𝕔 𝕓𝕔+𝕒𝕔𝕕 𝕓𝕔𝕕-𝕒𝕕 𝕓𝕕-𝕒𝕓𝕔 𝕔-𝕒𝕓𝕔𝕕 𝕔𝕕+𝕒𝕓𝕕 𝕕))^2)+(((ø 𝕒𝕔+𝕒𝕓𝕔 𝕓-𝕒𝕓 𝕓𝕔-𝕒𝕓𝕕 𝕓𝕔𝕕+𝕒𝕓𝕔𝕕 𝕓𝕕-𝕒 𝕔-𝕒𝕕 𝕔𝕕+𝕒𝕔𝕕 𝕕))^2)-(((ø 𝕒-𝕒𝕓 𝕓+𝕒𝕓𝕔 𝕓𝕔+𝕒𝕓𝕔𝕕 𝕓𝕔𝕕-𝕒𝕓𝕕 𝕓𝕕-𝕒𝕔 𝕔-𝕒𝕔𝕕 𝕔𝕕+𝕒𝕕 𝕕))^2)-(((-𝕒 𝕒𝕓𝕔𝕕-𝕒𝕓𝕕 𝕒𝕔+𝕒𝕓 𝕒𝕔𝕕+𝕒𝕓𝕔 𝕒𝕕+ø 𝕓𝕔𝕕+𝕓𝕕 𝕔-𝕓 𝕔𝕕-𝕓𝕔 𝕕))^2))}}});sd["CL04"]:=(el=Take[el2,16];rofu={};gi={1,-2,-3,-4,-5,-6,-7,8,-9,-10,-11,12,-13,14,15,16,4};gp=.;sh={{{((((ø^2)+(𝕒^2)+((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕓𝕔𝕕)^2)+((𝕒𝕓𝕕)^2)+((𝕒𝕔)^2)+((𝕒𝕔𝕕)^2)+((𝕒𝕕)^2)+(𝕓^2)+((𝕓𝕔)^2)+((𝕓𝕔𝕕)^2)+((𝕓𝕕)^2)+(𝕔^2)+((𝕔𝕕)^2)+(𝕕^2)))^2)-4 ((((ø 𝕒𝕓𝕕+𝕒𝕕 𝕓-𝕒𝕔𝕕 𝕓𝕔+𝕒𝕔 𝕓𝕔𝕕-𝕒 𝕓𝕕-𝕒𝕓𝕔𝕕 𝕔+𝕒𝕓𝕔 𝕔𝕕-𝕒𝕓 𝕕))^2)+(((ø 𝕒𝕓𝕔𝕕-𝕒𝕔𝕕 𝕓-𝕒𝕕 𝕓𝕔+𝕒 𝕓𝕔𝕕+𝕒𝕔 𝕓𝕕+𝕒𝕓𝕕 𝕔-𝕒𝕓 𝕔𝕕-𝕒𝕓𝕔 𝕕))^2)+(((ø 𝕒𝕓𝕔+𝕒𝕔 𝕓-𝕒 𝕓𝕔-𝕒𝕕 𝕓𝕔𝕕+𝕒𝕔𝕕 𝕓𝕕-𝕒𝕓 𝕔-𝕒𝕓𝕕 𝕔𝕕+𝕒𝕓𝕔𝕕 𝕕))^2)+(((ø 𝕒𝕔𝕕+𝕒𝕓𝕔𝕕 𝕓+𝕒𝕓𝕕 𝕓𝕔-𝕒𝕓 𝕓𝕔𝕕-𝕒𝕓𝕔 𝕓𝕕+𝕒𝕕 𝕔-𝕒 𝕔𝕕-𝕒𝕔 𝕕))^2)+(((-𝕒 𝕒𝕓𝕔𝕕-𝕒𝕓𝕕 𝕒𝕔+𝕒𝕓 𝕒𝕔𝕕+𝕒𝕓𝕔 𝕒𝕕+ø 𝕓𝕔𝕕+𝕓𝕕 𝕔-𝕓 𝕔𝕕-𝕓𝕔 𝕕))^2))}}});sd["CL40"]:=(el=Take[el2,16];rofu={};gi={1,2,3,-4,5,-6,-7,-8,9,-10,-11,-12,-13,-14,-15,16,4};gp=.;sh={{{((((ø^2)+(𝕒^2)+((𝕒𝕓)^2)+((𝕒𝕓𝕔)^2)+((𝕒𝕓𝕔𝕕)^2)+((𝕒𝕓𝕕)^2)+((𝕒𝕔)^2)+((𝕒𝕔𝕕)^2)+((𝕒𝕕)^2)+(𝕓^2)+((𝕓𝕔)^2)+((𝕓𝕔𝕕)^2)+((𝕓𝕕)^2)+(𝕔^2)+((𝕔𝕕)^2)+(𝕕^2)))^2)-4 ((((-𝕒𝕓𝕔 𝕒𝕓𝕔𝕕+𝕒𝕓 𝕒𝕓𝕕+𝕒𝕔 𝕒𝕔𝕕-𝕒 𝕒𝕕+𝕓𝕔 𝕓𝕔𝕕-𝕓 𝕓𝕕-𝕔 𝕔𝕕+ø 𝕕))^2)+(((ø 𝕒𝕓𝕔𝕕+𝕒𝕔𝕕 𝕓-𝕒𝕕 𝕓𝕔-𝕒 𝕓𝕔𝕕+𝕒𝕔 𝕓𝕕-𝕒𝕓𝕕 𝕔-𝕒𝕓 𝕔𝕕+𝕒𝕓𝕔 𝕕))^2)+(((ø 𝕒+𝕒𝕓 𝕓+𝕒𝕓𝕔 𝕓𝕔+𝕒𝕓𝕔𝕕 𝕓𝕔𝕕+𝕒𝕓𝕕 𝕓𝕕+𝕒𝕔 𝕔+𝕒𝕔𝕕 𝕔𝕕+𝕒𝕕 𝕕))^2)+(((-𝕒 𝕒𝕓-𝕒𝕓𝕔 𝕒𝕔-𝕒𝕓𝕔𝕕 𝕒𝕔𝕕-𝕒𝕓𝕕 𝕒𝕕+ø 𝕓+𝕓𝕔 𝕔+𝕓𝕔𝕕 𝕔𝕕+𝕓𝕕 𝕕))^2)+(((𝕒𝕓 𝕒𝕓𝕔+𝕒𝕓𝕔𝕕 𝕒𝕓𝕕-𝕒 𝕒𝕔-𝕒𝕔𝕕 𝕒𝕕-𝕓 𝕓𝕔-𝕓𝕔𝕕 𝕓𝕕+ø 𝕔+𝕔𝕕 𝕕))^2))}}});

sd["O8"]:=(el=Take[el2,16];rofu={};gp={1,0.,1,0.,1,0.,1,0.,1,0.,1,0.,1,0.,1,0.};gi={1,2,3,4,5,6,7,8,-9,-10,-11,-12,-13,-14,-15,-16,1,1,1,1,1,1,1,1};gp=.;sh={{{(((ø+𝕒+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2)+(((𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔𝕕+𝕒𝕕+𝕓𝕔𝕕+𝕓𝕕+𝕔𝕕+𝕕))^2)}},{{(((ø-𝕒+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓𝕔+𝕔))^2)+(((𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔𝕕-𝕒𝕕-𝕓𝕔𝕕-𝕓𝕕+𝕔𝕕+𝕕))^2)}},{{(((ø-𝕒-𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓+𝕓𝕔+𝕔))^2)+(((-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔𝕕-𝕒𝕕+𝕓𝕔𝕕+𝕓𝕕+𝕔𝕕+𝕕))^2)}},{{(((ø+𝕒-𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓-𝕓𝕔+𝕔))^2)+(((-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔𝕕+𝕒𝕕-𝕓𝕔𝕕-𝕓𝕕+𝕔𝕕+𝕕))^2)}},{{(((ø+𝕒+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕔+𝕓-𝕓𝕔-𝕔))^2)+(((-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕-𝕒𝕔𝕕+𝕒𝕕-𝕓𝕔𝕕+𝕓𝕕-𝕔𝕕+𝕕))^2)}},{{(((ø-𝕒+𝕒𝕓-𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓𝕔-𝕔))^2)+(((-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔𝕕-𝕒𝕕+𝕓𝕔𝕕-𝕓𝕕-𝕔𝕕+𝕕))^2)}},{{(((ø-𝕒-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔+𝕓-𝕓𝕔-𝕔))^2)+(((𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔𝕕-𝕒𝕕-𝕓𝕔𝕕+𝕓𝕕-𝕔𝕕+𝕕))^2)}},{{(((ø+𝕒-𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔-𝕓+𝕓𝕔-𝕔))^2)+(((𝕒𝕓𝕔𝕕-𝕒𝕓𝕕-𝕒𝕔𝕕+𝕒𝕕+𝕓𝕔𝕕-𝕓𝕕-𝕔𝕕+𝕕))^2)}}});toPol[{a_,b_,c_,d_,e_,f_,g_,h_,i_,j_,k_,l_,m_,n_,o_,p_},"O8"]:= {      (((a+b+c+d+e+f+g+h))^2)+(((i+j+k+l+m+n+o+p))^2),ArcTan[a+b+c+d+e+f+g+h,i+j+k+l+m+n+o+p],
      (((a-b-c+d+e-f-g+h))^2)+(((i-j-k+l+m-n-o+p))^2),ArcTan[a-b-c+d+e-f-g+h,i-j-k+l+m-n-o+p],
      (((a-b+c-d+e-f+g-h))^2)+(((i-j+k-l+m-n+o-p))^2),ArcTan[a-b+c-d+e-f+g-h,i-j+k-l+m-n+o-p],
      (((a+b-c-d+e+f-g-h))^2)+(((i+j-k-l+m+n-o-p))^2),ArcTan[a+b-c-d+e+f-g-h,i+j-k-l+m+n-o-p],
      (((a+b+c+d-e-f-g-h))^2)+(((i+j+k+l-m-n-o-p))^2),ArcTan[a+b+c+d-e-f-g-h,i+j+k+l-m-n-o-p],
      (((a-b-c+d-e+f+g-h))^2)+(((i-j-k+l-m+n+o-p))^2),ArcTan[a-b-c+d-e+f+g-h,i-j-k+l-m+n+o-p],
       (((a-b+c-d-e+f-g+h))^2)+(((i-j+k-l-m+n-o+p))^2),ArcTan[a-b+c-d-e+f-g+h,i-j+k-l-m+n-o+p],
       (((a+b-c-d-e-f+g+h))^2)+(((i+j-k-l-m-n+o+p))^2),ArcTan[a+b-c-d-e-f+g+h,i+j-k-l-m-n+o+p]};toVec[{ii_,j_,kk_,l_,mm_,n_,oo_,p_,qq_,r_,ss_,t_,uu_,v_,ww_,x_},"O8"]:=Module[{i=(Sqrt[ii]),k=(Sqrt[kk]),m=(Sqrt[mm]),o=(Sqrt[oo]),q=(Sqrt[qq]),s=(Sqrt[ss]),u=(Sqrt[uu]),w=(Sqrt[ww])},2{i Cos[j]+k Cos[l]+m Cos[n]+o Cos[p]+q Cos[r]+s Cos[t]+u Cos[v]+w Cos[x],
i Cos[j]-k Cos[l]-m Cos[n]+o Cos[p]+q Cos[r]-s Cos[t]-u Cos[v]+w Cos[x],
i Cos[j]-k Cos[l]+m Cos[n]-o Cos[p]+q Cos[r]-s Cos[t]+u Cos[v]-w Cos[x],
i Cos[j]+k Cos[l]-m Cos[n]-o Cos[p]+q Cos[r]+s Cos[t]-u Cos[v]-w Cos[x],
i Cos[j]+k Cos[l]+m Cos[n]+o Cos[p]-q Cos[r]-s Cos[t]-u Cos[v]-w Cos[x],
i Cos[j]-k Cos[l]-m Cos[n]+o Cos[p]-q Cos[r]+s Cos[t]+u Cos[v]-w Cos[x],
i Cos[j]-k Cos[l]+m Cos[n]-o Cos[p]-q Cos[r]+s Cos[t]-u Cos[v]+w Cos[x],
i Cos[j]+k Cos[l]-m Cos[n]-o Cos[p]-q Cos[r]-s Cos[t]+u Cos[v]+w Cos[x],
i Sin[j]+k Sin[l]+m Sin[n]+o Sin[p]+q Sin[r]+s Sin[t]+u Sin[v]+w Sin[x],
i Sin[j]-k Sin[l]-m Sin[n]+o Sin[p]+q Sin[r]-s Sin[t]-u Sin[v]+w Sin[x],
i Sin[j]-k Sin[l]+m Sin[n]-o Sin[p]+q Sin[r]-s Sin[t]+u Sin[v]-w Sin[x],
i Sin[j]+k Sin[l]-m Sin[n]-o Sin[p]+q Sin[r]+s Sin[t]-u Sin[v]-w Sin[x],
i Sin[j]+k Sin[l]+m Sin[n]+o Sin[p]-q Sin[r]-s Sin[t]-u Sin[v]-w Sin[x],
i Sin[j]-k Sin[l]-m Sin[n]+o Sin[p]-q Sin[r]+s Sin[t]+u Sin[v]-w Sin[x],
i Sin[j]-k Sin[l]+m Sin[n]-o Sin[p]-q Sin[r]+s Sin[t]-u Sin[v]+w Sin[x],
i Sin[j]+k Sin[l]-m Sin[n]-o Sin[p]-q Sin[r]-s Sin[t]+u Sin[v]+w Sin[x]}/16];

9.12 Shapes for larger tables.

sd["D18"]:=(gi={1,2,17,4,15,6,13,8,11,10,9,12,7,14,5,16,3,18,1,1,2,2,2,2,2,2,2,2};el=Take[e33,18];rofu=rU[[2]]⋃rU[[5]];sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2+𝕒2𝕓2𝕔+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓2+𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓2+𝕓2𝕔+𝕓𝕔+𝕔}},{{ø-𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2-𝕒2𝕓2𝕔-𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓-𝕒𝕓2+𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔-𝕓+𝕓2-𝕓2𝕔+𝕓𝕔-𝕔}},{{ø+(𝕐^2) 𝕒2+𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+𝕐 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔+𝕐 𝕒𝕔+𝕐 𝕓2+𝕓𝕔,(𝕐^2) 𝕒+𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+(𝕐^2) 𝕒𝕓2+𝕐 𝕓+(𝕐^2) 𝕓2𝕔+𝕐 𝕔},{𝕐 𝕒+𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕐 𝕒𝕓2+(𝕐^2) 𝕓+𝕐 𝕓2𝕔+(𝕐^2) 𝕔,ø+𝕐 𝕒2+𝕒2𝕓+𝕐 𝕒2𝕓2+(𝕐^2) 𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔+(𝕐^2) 𝕒𝕔+(𝕐^2) 𝕓2+𝕓𝕔}},{{ø-(𝕟^2)-(𝕟^4)+(𝕟^2) 𝕒2+(𝕐^2) 𝕒2𝕓-(𝕟^5) 𝕒2𝕓2+(𝕟^7) 𝕒𝕓2𝕔+(𝕟^5) 𝕒𝕓𝕔-(𝕟^7) 𝕒𝕔+(𝕟^4) 𝕓2+𝕐 𝕓𝕔,-(𝕟^2)-(𝕟^4)+(𝕟^2) 𝕒+𝕒2𝕓2𝕔+(𝕟^7) 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+(𝕐^2) 𝕒𝕓-(𝕟^5) 𝕒𝕓2+(𝕟^4) 𝕓+(𝕟^5) 𝕓2𝕔-(𝕟^7) 𝕔},{-(𝕟^2)-(𝕟^4)+(𝕟^7) 𝕒+𝕒2𝕓2𝕔+(𝕟^2) 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕐 𝕒𝕓-(𝕟^7) 𝕒𝕓2+(𝕟^5) 𝕓+(𝕟^4) 𝕓2𝕔-(𝕟^5) 𝕔,ø-(𝕟^2)-(𝕟^4)+(𝕟^7) 𝕒2+𝕐 𝕒2𝕓-(𝕟^7) 𝕒2𝕓2+(𝕟^2) 𝕒𝕓2𝕔+(𝕟^4) 𝕒𝕓𝕔-(𝕟^5) 𝕒𝕔+(𝕟^5) 𝕓2+(𝕐^2) 𝕓𝕔}},{{ø-(𝕟^2)-(𝕟^4)+(𝕟^5) 𝕒2+(𝕐^2) 𝕒2𝕓+(𝕟^2) 𝕒2𝕓2+(𝕟^4) 𝕒𝕓2𝕔-(𝕟^5) 𝕒𝕓𝕔+(𝕟^7) 𝕒𝕔-(𝕟^7) 𝕓2+𝕐 𝕓𝕔,-(𝕟^2)-(𝕟^4)+(𝕟^5) 𝕒+𝕒2𝕓2𝕔+(𝕟^4) 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+(𝕐^2) 𝕒𝕓+(𝕟^2) 𝕒𝕓2-(𝕟^7) 𝕓-(𝕟^5) 𝕓2𝕔+(𝕟^7) 𝕔},{-(𝕟^2)-(𝕟^4)+(𝕟^4) 𝕒+𝕒2𝕓2𝕔+(𝕟^5) 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕐 𝕒𝕓+(𝕟^7) 𝕒𝕓2-(𝕟^5) 𝕓-(𝕟^7) 𝕓2𝕔+(𝕟^2) 𝕔,ø-(𝕟^2)-(𝕟^4)+(𝕟^4) 𝕒2+𝕐 𝕒2𝕓+(𝕟^7) 𝕒2𝕓2+(𝕟^5) 𝕒𝕓2𝕔-(𝕟^7) 𝕒𝕓𝕔+(𝕟^2) 𝕒𝕔-(𝕟^5) 𝕓2+(𝕐^2) 𝕓𝕔}},{{ø-(𝕟^2)-(𝕟^4)-(𝕟^7) 𝕒2+𝕐 𝕒2𝕓+(𝕟^4) 𝕒2𝕓2-(𝕟^5) 𝕒𝕓2𝕔+(𝕟^7) 𝕒𝕓𝕔+(𝕟^5) 𝕒𝕔+(𝕟^2) 𝕓2+(𝕐^2) 𝕓𝕔,-(𝕟^2)-(𝕟^4)-(𝕟^7) 𝕒+𝕒2𝕓2𝕔-(𝕟^5) 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕐 𝕒𝕓+(𝕟^4) 𝕒𝕓2+(𝕟^2) 𝕓+(𝕟^7) 𝕓2𝕔+(𝕟^5) 𝕔},{-(𝕟^2)-(𝕟^4)-(𝕟^5) 𝕒+𝕒2𝕓2𝕔-(𝕟^7) 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+(𝕐^2) 𝕒𝕓+(𝕟^5) 𝕒𝕓2+(𝕟^7) 𝕓+(𝕟^2) 𝕓2𝕔+(𝕟^4) 𝕔,ø-(𝕟^2)-(𝕟^4)-(𝕟^5) 𝕒2+(𝕐^2) 𝕒2𝕓+(𝕟^5) 𝕒2𝕓2-(𝕟^7) 𝕒𝕓2𝕔+(𝕟^2) 𝕒𝕓𝕔+(𝕟^4) 𝕒𝕔+(𝕟^7) 𝕓2+𝕐 𝕓𝕔}}});

sd["C6C3"]:=(gi={1,3,2,4,6,5,13,15,14,16,18,17,13,15,14,16,18,17,1,1,2,6};el=Take[e33,18];rofu=rU[[2]];sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2+𝕒2𝕓2𝕔+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓2+𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓2+𝕓2𝕔+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2-𝕒2𝕓2𝕔-𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓+𝕒𝕓2-𝕒𝕓2𝕔+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓2+𝕓2𝕔+𝕓𝕔-𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+(𝕐^2) 𝕒2𝕓+𝕒2𝕓2-(𝕐^2) 𝕒2𝕓2𝕔-𝕐 𝕒2𝕓𝕔-𝕒2𝕔-𝕐 𝕒𝕓+𝕐 𝕒𝕓2-𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔-𝕐 𝕒𝕔-𝕓-(𝕐^2) 𝕓2+𝕓2𝕔+𝕐 𝕓𝕔-(𝕐^2) 𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕐 𝕒2𝕓+𝕒2𝕓2-𝕐 𝕒2𝕓2𝕔-(𝕐^2) 𝕒2𝕓𝕔-𝕒2𝕔-(𝕐^2) 𝕒𝕓+(𝕐^2) 𝕒𝕓2-𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔-(𝕐^2) 𝕒𝕔-𝕓-𝕐 𝕓2+𝕓2𝕔+(𝕐^2) 𝕓𝕔-𝕐 𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕐 𝕒2𝕓+𝕒2𝕓2+𝕐 𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+𝕒2𝕔+(𝕐^2) 𝕒𝕓+(𝕐^2) 𝕒𝕓2+𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔+(𝕐^2) 𝕒𝕔+𝕓+𝕐 𝕓2+𝕓2𝕔+(𝕐^2) 𝕓𝕔+𝕐 𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+(𝕐^2) 𝕒2𝕓+𝕒2𝕓2+(𝕐^2) 𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+𝕒2𝕔+𝕐 𝕒𝕓+𝕐 𝕒𝕓2+𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔+𝕐 𝕒𝕔+𝕓+(𝕐^2) 𝕓2+𝕓2𝕔+𝕐 𝕓𝕔+(𝕐^2) 𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕒2𝕓+(𝕐^2) 𝕒2𝕓2-(𝕐^2) 𝕒2𝕓2𝕔-𝕒2𝕓𝕔-(𝕐^2) 𝕒2𝕔-(𝕐^2) 𝕒𝕓+𝕐 𝕒𝕓2-𝕐 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔-𝕐 𝕒𝕔-𝕓-𝕐 𝕓2+𝕐 𝕓2𝕔+𝕓𝕔-𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕒2𝕓+𝕐 𝕒2𝕓2-𝕐 𝕒2𝕓2𝕔-𝕒2𝕓𝕔-𝕐 𝕒2𝕔-𝕐 𝕒𝕓+(𝕐^2) 𝕒𝕓2-(𝕐^2) 𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔-(𝕐^2) 𝕒𝕔-𝕓-(𝕐^2) 𝕓2+(𝕐^2) 𝕓2𝕔+𝕓𝕔-𝕔}},{{ø+𝕒+𝕒2+(𝕐^2) 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2-𝕐 𝕒2𝕓2𝕔-𝕐 𝕒2𝕓𝕔-(𝕐^2) 𝕒2𝕔-𝕒𝕓+(𝕐^2) 𝕒𝕓2-𝕐 𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔-(𝕐^2) 𝕒𝕔-𝕓-𝕓2+𝕐 𝕓2𝕔+𝕐 𝕓𝕔-(𝕐^2) 𝕔}},{{ø+𝕒+𝕒2+𝕐 𝕒2𝕓+𝕐 𝕒2𝕓2-(𝕐^2) 𝕒2𝕓2𝕔-(𝕐^2) 𝕒2𝕓𝕔-𝕐 𝕒2𝕔-𝕒𝕓+𝕐 𝕒𝕓2-(𝕐^2) 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔-𝕐 𝕒𝕔-𝕓-𝕓2+(𝕐^2) 𝕓2𝕔+(𝕐^2) 𝕓𝕔-𝕐 𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕐 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2-𝕒2𝕓2𝕔-(𝕐^2) 𝕒2𝕓𝕔-(𝕐^2) 𝕒2𝕔-𝕐 𝕒𝕓+𝕒𝕓2-𝕐 𝕒𝕓2𝕔+𝕒𝕓𝕔-𝕒𝕔-𝕓-(𝕐^2) 𝕓2+𝕐 𝕓2𝕔+(𝕐^2) 𝕓𝕔-𝕐 𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+(𝕐^2) 𝕒2𝕓+𝕐 𝕒2𝕓2-𝕒2𝕓2𝕔-𝕐 𝕒2𝕓𝕔-𝕐 𝕒2𝕔-(𝕐^2) 𝕒𝕓+𝕒𝕓2-(𝕐^2) 𝕒𝕓2𝕔+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕐 𝕓2+(𝕐^2) 𝕓2𝕔+𝕐 𝕓𝕔-(𝕐^2) 𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕒2𝕓+𝕐 𝕒2𝕓2+𝕐 𝕒2𝕓2𝕔+𝕒2𝕓𝕔+𝕐 𝕒2𝕔+𝕐 𝕒𝕓+(𝕐^2) 𝕒𝕓2+(𝕐^2) 𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔+(𝕐^2) 𝕒𝕔+𝕓+(𝕐^2) 𝕓2+(𝕐^2) 𝕓2𝕔+𝕓𝕔+𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+(𝕐^2) 𝕒2𝕓2𝕔+𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+(𝕐^2) 𝕒𝕓+𝕐 𝕒𝕓2+𝕐 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔+𝕐 𝕒𝕔+𝕓+𝕐 𝕓2+𝕐 𝕓2𝕔+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2+𝕐 𝕒2𝕓+𝕐 𝕒2𝕓2+(𝕐^2) 𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+𝕒𝕓+𝕐 𝕒𝕓2+(𝕐^2) 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕓𝕔+𝕐 𝕒𝕔+𝕓+𝕓2+(𝕐^2) 𝕓2𝕔+(𝕐^2) 𝕓𝕔+𝕐 𝕔}},{{ø+𝕒+𝕒2+(𝕐^2) 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+𝕐 𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕒𝕓+(𝕐^2) 𝕒𝕓2+𝕐 𝕒𝕓2𝕔+𝕐 𝕒𝕓𝕔+(𝕐^2) 𝕒𝕔+𝕓+𝕓2+𝕐 𝕓2𝕔+𝕐 𝕓𝕔+(𝕐^2) 𝕔}},{{ø+𝕐 𝕒+(𝕐^2) 𝕒2+(𝕐^2) 𝕒2𝕓+𝕐 𝕒2𝕓2+𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+(𝕐^2) 𝕒𝕓+𝕒𝕓2+(𝕐^2) 𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕐 𝕓2+(𝕐^2) 𝕓2𝕔+𝕐 𝕓𝕔+(𝕐^2) 𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕐 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕐 𝕒𝕓+𝕒𝕓2+𝕐 𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔+𝕓+(𝕐^2) 𝕓2+𝕐 𝕓2𝕔+(𝕐^2) 𝕓𝕔+𝕐 𝕔}}});

sd["C3C3iC2"]:=(gi={1,3,2,4,5,6,13,15,14,10,11,12,7,9,8,16,17,18,1,1,2,2,2,2};el=Take[e33,18];rofu=rU[[2]];sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2+𝕒2𝕓2𝕔+𝕒2𝕓𝕔+𝕒2𝕔+𝕒𝕓+𝕒𝕓2+𝕒𝕓2𝕔+𝕒𝕓𝕔+𝕒𝕔+𝕓+𝕓2+𝕓2𝕔+𝕓𝕔+𝕔}},{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓2-𝕒2𝕓2𝕔-𝕒2𝕓𝕔-𝕒2𝕔-𝕒𝕓+𝕒𝕓2-𝕒𝕓2𝕔+𝕒𝕓𝕔-𝕒𝕔-𝕓-𝕓2+𝕓2𝕔+𝕓𝕔-𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕐 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+𝕒𝕓2+𝕒𝕓𝕔+𝕐 𝕓2𝕔+(𝕐^2) 𝕓𝕔,(𝕐^2) 𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+𝕒2𝕔+𝕐 𝕒𝕓+𝕒𝕓2𝕔+𝕐 𝕒𝕔+𝕓+(𝕐^2) 𝕓2+(𝕐^2) 𝕔},{𝕐 𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+𝕒2𝕔+(𝕐^2) 𝕒𝕓+𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕔+𝕓+𝕐 𝕓2+𝕐 𝕔,ø+𝕐 𝕒+(𝕐^2) 𝕒2+(𝕐^2) 𝕒2𝕓+𝕐 𝕒2𝕓2+𝕒𝕓2+𝕒𝕓𝕔+(𝕐^2) 𝕓2𝕔+𝕐 𝕓𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+(𝕐^2) 𝕒2𝕓+𝕒2𝕓2+𝕐 𝕒𝕓2+(𝕐^2) 𝕒𝕓𝕔+𝕓2𝕔+𝕐 𝕓𝕔,𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕐 𝕒𝕓+𝕐 𝕒𝕓2𝕔+𝕒𝕔+𝕓+(𝕐^2) 𝕓2+𝕐 𝕔},{𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+(𝕐^2) 𝕒𝕓+(𝕐^2) 𝕒𝕓2𝕔+𝕒𝕔+𝕓+𝕐 𝕓2+(𝕐^2) 𝕔,ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕐 𝕒2𝕓+𝕒2𝕓2+(𝕐^2) 𝕒𝕓2+𝕐 𝕒𝕓𝕔+𝕓2𝕔+(𝕐^2) 𝕓𝕔}},{{ø+𝕒+𝕒2+(𝕐^2) 𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+(𝕐^2) 𝕒𝕓2+𝕐 𝕒𝕓𝕔+𝕐 𝕓2𝕔+𝕐 𝕓𝕔,(𝕐^2) 𝕒2𝕓2𝕔+(𝕐^2) 𝕒2𝕓𝕔+𝕐 𝕒2𝕔+𝕒𝕓+(𝕐^2) 𝕒𝕓2𝕔+𝕐 𝕒𝕔+𝕓+𝕓2+𝕐 𝕔},{𝕐 𝕒2𝕓2𝕔+𝕐 𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+𝕒𝕓+𝕐 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕔+𝕓+𝕓2+(𝕐^2) 𝕔,ø+𝕒+𝕒2+𝕐 𝕒2𝕓+𝕐 𝕒2𝕓2+𝕐 𝕒𝕓2+(𝕐^2) 𝕒𝕓𝕔+(𝕐^2) 𝕓2𝕔+(𝕐^2) 𝕓𝕔}},{{ø+(𝕐^2) 𝕒+𝕐 𝕒2+𝕒2𝕓+𝕐 𝕒2𝕓2+(𝕐^2) 𝕒𝕓2+𝕐 𝕒𝕓𝕔+(𝕐^2) 𝕓2𝕔+𝕓𝕔,𝕐 𝕒2𝕓2𝕔+𝕒2𝕓𝕔+𝕐 𝕒2𝕔+𝕐 𝕒𝕓+(𝕐^2) 𝕒𝕓2𝕔+(𝕐^2) 𝕒𝕔+𝕓+(𝕐^2) 𝕓2+𝕔},{(𝕐^2) 𝕒2𝕓2𝕔+𝕒2𝕓𝕔+(𝕐^2) 𝕒2𝕔+(𝕐^2) 𝕒𝕓+𝕐 𝕒𝕓2𝕔+𝕐 𝕒𝕔+𝕓+𝕐 𝕓2+𝕔,ø+𝕐 𝕒+(𝕐^2) 𝕒2+𝕒2𝕓+(𝕐^2) 𝕒2𝕓2+𝕐 𝕒𝕓2+(𝕐^2) 𝕒𝕓𝕔+𝕐 𝕓2𝕔+𝕓𝕔}}});

sd["S4"]:=(gi={1,2,3,5,4,6,7,8,13,19,14,20,9,11,15,21,17,23,10,12,16,22,18,24, 1,1,2,3,3};el=Take[el3,24];rofu=rU[[2]];sh={{{ø+𝕒+𝕒2+𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕓𝕔𝕕+𝕒2𝕓𝕕+𝕒2𝕔+𝕒2𝕔𝕕+𝕒2𝕕+𝕒𝕓+𝕒𝕓𝕔+𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕+𝕒𝕕+𝕓+𝕓𝕔+𝕓𝕔𝕕+𝕓𝕕+𝕔+𝕔𝕕+𝕕}},{{ø-𝕒-𝕒2-𝕒2𝕓+𝕒2𝕓𝕔+𝕒2𝕓𝕔𝕕-𝕒2𝕓𝕕+𝕒2𝕔+𝕒2𝕔𝕕-𝕒2𝕕+𝕒𝕓-𝕒𝕓𝕔-𝕒𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒𝕔𝕕-𝕒𝕕+𝕓-𝕓𝕔-𝕓𝕔𝕕+𝕓𝕕-𝕔-𝕔𝕕+𝕕}},{{ø+𝕒2𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒2𝕓𝕔 𝕐+𝕒2𝕔𝕕 𝕐+𝕓 𝕐+𝕕 𝕐+𝕒2𝕔 (𝕐^2)+𝕒𝕓 (𝕐^2)+𝕒𝕔𝕕 (𝕐^2)+𝕓𝕕 (𝕐^2),𝕒+𝕒2𝕓𝕕+𝕒𝕓𝕔𝕕+𝕔+𝕒2 𝕐+𝕒𝕓𝕔 𝕐+𝕒𝕕 𝕐+𝕓𝕔𝕕 𝕐+𝕒2𝕓 (𝕐^2)+𝕒2𝕕 (𝕐^2)+𝕓𝕔 (𝕐^2)+𝕔𝕕 (𝕐^2)},{𝕒+𝕒2𝕓𝕕+𝕒𝕓𝕔𝕕+𝕔+𝕒2𝕓 𝕐+𝕒2𝕕 𝕐+𝕓𝕔 𝕐+𝕔𝕕 𝕐+𝕒2 (𝕐^2)+𝕒𝕓𝕔 (𝕐^2)+𝕒𝕕 (𝕐^2)+𝕓𝕔𝕕 (𝕐^2),ø+𝕒2𝕓𝕔𝕕+𝕒𝕓𝕕+𝕒𝕔+𝕒2𝕔 𝕐+𝕒𝕓 𝕐+𝕒𝕔𝕕 𝕐+𝕓𝕕 𝕐+𝕒2𝕓𝕔 (𝕐^2)+𝕒2𝕔𝕕 (𝕐^2)+𝕓 (𝕐^2)+𝕕 (𝕐^2)}},{{ø+𝕒2+𝕒2𝕓𝕔𝕕-𝕒𝕓𝕔-𝕒𝕓𝕕-𝕒𝕔-𝕒𝕕+𝕓𝕔𝕕,-𝕒+𝕒2𝕓𝕔+𝕒2𝕓𝕕-𝕒2𝕔𝕕-𝕒𝕓𝕔𝕕-𝕓+𝕔+𝕕,-𝕒2𝕓+𝕒2𝕔+𝕒2𝕕-𝕒𝕓-𝕒𝕔𝕕+𝕓𝕔+𝕓𝕕-𝕔𝕕},{-𝕒-𝕒2𝕓𝕕+𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔𝕕+𝕒𝕔𝕕-𝕓𝕕+𝕔,ø+𝕒2𝕓-𝕒2𝕓𝕔𝕕+𝕒2𝕕+𝕒𝕓𝕕-𝕒𝕔-𝕓𝕔-𝕔𝕕,𝕒2-𝕒2𝕓𝕔-𝕒2𝕔𝕕-𝕒𝕓𝕔+𝕒𝕕+𝕓-𝕓𝕔𝕕+𝕕},{-𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔𝕕+𝕒2𝕕-𝕓-𝕓𝕔+𝕔𝕕+𝕕,𝕒2+𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔-𝕒𝕔𝕕-𝕒𝕕-𝕓𝕔𝕕-𝕓𝕕,ø+𝕒-𝕒2𝕓𝕔𝕕-𝕒2𝕓𝕕-𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔+𝕔}},{{ø-𝕒2+𝕒2𝕓𝕔𝕕+𝕒𝕓𝕔-𝕒𝕓𝕕-𝕒𝕔+𝕒𝕕-𝕓𝕔𝕕,-𝕒-𝕒2𝕓𝕔+𝕒2𝕓𝕕+𝕒2𝕔𝕕-𝕒𝕓𝕔𝕕+𝕓+𝕔-𝕕,𝕒2𝕓+𝕒2𝕔-𝕒2𝕕-𝕒𝕓-𝕒𝕔𝕕-𝕓𝕔+𝕓𝕕+𝕔𝕕},{-𝕒-𝕒2𝕓𝕕-𝕒2𝕔+𝕒𝕓+𝕒𝕓𝕔𝕕-𝕒𝕔𝕕+𝕓𝕕+𝕔,ø-𝕒2𝕓-𝕒2𝕓𝕔𝕕-𝕒2𝕕+𝕒𝕓𝕕-𝕒𝕔+𝕓𝕔+𝕔𝕕,𝕒2+𝕒2𝕓𝕔+𝕒2𝕔𝕕-𝕒𝕓𝕔+𝕒𝕕-𝕓-𝕓𝕔𝕕-𝕕},{𝕒2𝕓-𝕒2𝕓𝕔+𝕒2𝕔𝕕-𝕒2𝕕-𝕓+𝕓𝕔-𝕔𝕕+𝕕,𝕒2-𝕒2𝕔-𝕒𝕓+𝕒𝕓𝕔+𝕒𝕔𝕕-𝕒𝕕-𝕓𝕔𝕕+𝕓𝕕,ø-𝕒-𝕒2𝕓𝕔𝕕+𝕒2𝕓𝕕+𝕒𝕓𝕔𝕕-𝕒𝕓𝕕+𝕒𝕔-𝕔}}})

9.14 sd[_]

(*sd[_]=sd[gName]; *)sd[z_]=(el=.;rofu={};gi={};gp={};sh={{{}}});(* only reached if gName sd is unknown*)

sd[1];(*initialise el etc.*)

10. Exported functions.

10.1 Loop Procedures abbr, cosorbit, fold, gpd, isoCay, shape, tidy, toSignedTable,proto, ω=2π/3.

abbr[t_,o_:1,n_:{}]:=Module[{a={},l=Length[t]-1,f=First[t],r=Drop[t,1],s,u=Union[Drop[t,1]],ui},Do[ui=u[[i]];s=Length[Position[r,ui]] ;If[s>1,u[[i]]=(Subscript[ui, s])],{i,Length[u]}];Flatten[Join[{o f},u,n]]];

addSigns[g_,n_]:=Module[{l=Length[g]},rr={};Do[(*i*)Which[n==2,AppendTo[rr,i+l->-i],
n==3,AppendTo[rr,i+l->𝕁 i];AppendTo[rr,i+2 l->(𝕁^2) i],
n==4,AppendTo[rr,i+l->I i];AppendTo[rr,i+2 l->-i];AppendTo[rr,i+3 l->-I i],
n==6,AppendTo[rr,i+l->𝕙 i];AppendTo[rr,i+2 l->(𝕙^2)i];
AppendTo[rr,i+3l->(𝕙^3) i];AppendTo[rr,i+4 l->(𝕙^4) i];AppendTo[rr,i+5 l->(𝕙^5) i],
n==8,AppendTo[rr,i+l->𝕠 i];AppendTo[rr,i+2 l->(𝕠^2)i];
AppendTo[rr,i+3l->(𝕠^3) i];AppendTo[rr,i+4 l->(𝕠^4) i];AppendTo[rr,i+5 l->(𝕠^5) i];AppendTo[rr,i+6 l->(𝕠^6) i];AppendTo[rr,i+7 l->(𝕠^7) i]],{i,l}];
mm=l;Table[g[[i,j]]/.rr,{i,l},{j,l}]];

fold[g_,fo_:{2}]:=Module[{c,cen={},cenord={},indx,j,ji,jj,known,l=Length[g],lf,ordr,orders={},res={},rj={}},
Do[c=g[[i,1]];j=1;While[g[[c,j]]==g[[j,c]]&&j<l,j++];
If[j==l,AppendTo[cen,c]],{i,l}];
Do[c=1;j=cen[[i]];k=1;While[(k=g[[j,k]])≠1&&c<9999,c++];AppendTo[cenord,{cen[[i]],c}],{i,2,Length[cen]}];If[cenord=={},Print["No center"];Return[{}],
Do[(*j*)known={};
indx=cenord[[j,1]];ordr=cenord[[j,2]];
Do[(*i*)If[!MemberQ[known,i],jj=i;
Do[(*k*)AppendTo[known,jj];jj=g[[jj,indx]],
{k,ordr}]],{i,l}];
AppendTo[rj,Transpose[Partition[known,ordr]][[1]]];AppendTo[orders,ordr],{j,Length[cenord]}];Do[(*f*)f2=Position[orders,fo[[f]]];
If[f2!={}(*&&MemberQ[{2,3,4},fo[[f]]]*),gr=reorder[g,rj[[im=f2[[1,1]]]]];
AppendTo[res,addSigns[gr,orders[[im]]]]];
,{f,lf=Length[fo]}];res]];

gpd[gg_]:=Module[{g},If[gg=={{1}},Return[gg]];g=If[Length[gg]==1&&Head[gg]===TraditionalForm,gg[[1]],gg];If[Length[g]==Length[g[[1]]]&&(MatrixQ[g[[1,1]]]||Union[Flatten[Abs[g],1]]==Sort[Abs[g[[1]]]])||Length[Position[g,𝕁]]>0||Length[Position[g,𝕐]]>0,g,Print[Short[g]," is not a groupoid"];Abort[]]];

isoCay[g1_,g2_]:=Module[{},cay1=g1;cay2=g2;i1={};i2={};itn=0;isoCay[]];
isoCay[]:=(*From G.Gerrard's GAP routine.*)Catch[Module[{m=Length[i1],n=Length[cay1],p1,p2,loc1,loc2,perm},
If[dic[cay1]≠dic[cay2],Throw[False]];
itn++;If[itn>999,Abort[]];(*Recursion depth control*)
Do[(*ii*)
Do[(*jj*)p1=cay1[[i1[[ii]],i1[[jj]]]];
p2=cay2[[i2[[ii]],i2[[jj]]]];
If[(loc1=Position[i1,p1])=={},loc1=0,loc1=loc1[[1,1]]];
If[(loc2=Position[i2,p2])=={},loc2=0,loc2=loc2[[1,1]]];
If[loc1==0&&loc2==0,AppendTo[i1,p1];AppendTo[i2,p2];
If[isoCay[],Throw[True]];
i1=Most[i1];i2=Most[i2];Throw[False],
If[!(loc1>0&&loc2>0&&loc1==loc2),Throw[False]](*Else Continue*)]
,{jj,m,1,-1}]
,{ii,m,1,-1}];
If[Length[cay1]==Length[i2],c2Toc1=Table[i2[[Position[i1,i][[1,1]]]],{i,Length[i1]}];c1Toc2=Table[i1[[Position[i2,i][[1,1]]]],{i,Length[i2]}];Throw[True]];
AppendTo[i1,First[Complement[Range[n],i1]]];
Do[If[!MemberQ[i2,ii],AppendTo[i2,ii];
If[isoCay[],Throw[True],(*Else*)i2=Most[i2]]]
,{ii,1,n}];
i1=Most[i1];Throw[False]]];

shape[a_?VectorQ,g_:gName]:=Module[{shel},sd[g];shel=sh/.fromVtoA[el,a];Chop[Table[Expand[Det[shel[[i]]]/.rofu],{i,Length[sh]}],hmin]];
shape[a_]:=shape[tocFlat[a],gName];

tidy[gg_?indexTableQ,n_:-1,o_:1,p_:{}]:=Module[{a,b,c,d,g=If[Length[gg]==1,gg[[1]],gg],gl,m,nb,r,q},gl=Length[g];
If[Length[n]==0,b=subgroups[g][[-n]],b=n,b=n]; (* Find subgroup if list not supplied *)
nb=Length[b];m=gl/nb; If[!IntegerQ[m],Abort[]];  (* nb must divide gl *)
r=Complement[Range[gl],b];If[MemberQ[r,o],b=Join[b,{o}]];r=Complement[r,b];c=Join[b,r];b=c;d=Transpose[reorder[g,c]][[nb+1]];(* Run to find column for sorting *)
Do[b[[j+nb]]=c[[d[[j]]]],{j,2,nb}]; (* Rearrange col nb+1 *)
If[m>2,b=Take[b,2nb];r=Complement[Range[gl],b];
If[Length[p]>1,b=Join[b,p];b=Join[b,Complement[Range[gl],b]],
If[MemberQ[r,p],b=Join[b,{p}]];
b=Join[b,Complement[r,b]]]];(* Add other elements *)
Print[b];reorder[g,b]]

ts[a___]:=toSignedTable[a];toSignedTable[g_?indexTableQ,r_Integer:2,reo_:{},o_:0]:=Module[{diags,diagelements,dis,gg=g,i,j,l=Length[g],nex=1,n=Abs[r],ps,rr={},res,s},el=Take[el2,Floor[l/r]];If[reo≠{},gg=reorder[gg,reo];If[o>1,Print[{"reordered",tf[gg]}]]];If[Length[gg]===Length[g],If[negatableQ[gg,n]==True,If[o>2,Print[{"Immediately ",n,"negatable"}]];gg=Take[Transpose[Take[gg,(l/n)]],(l/n)],diags=Table[gg[[ii,ii]],{ii,l}];diagelements=Union[diags];If[o≠0,Print[{diags,"diags,elems",diagelements}]];res=Table[0,{(l/n)}];Do[(*jj*)If[Mod[Length[diagelements[[jj]]],n]≠0,Print[{"not ",n,"negatable"}];Abort[],ps=Position[diags,Union[diagelements][[jj]]];If[o>1,Print[{"ps,jj,nex",ps,jj,nex}]];If[Mod[Length[ps],n]≠0,Print[{"not ",n,"negatable"}];Abort[]];Do[(*nx*)res[[nex]]=ps[[nx]];nex++,{nx,((Length[ps])/n)}]](*endIf*);If[o≠0,Print[Flatten[{"res",res}]]],{jj,Length[(diagelements/n)]}];gg=reorder[g,Flatten[res]]]];s=Length[gg];i=.;rr={};Do[(*i*)Which[n==2,AppendTo[rr,i+s->-i],
n==3,AppendTo[rr,i+s->𝕐 i];AppendTo[rr,i+2 s->𝕐 𝕐 i],
n==4,AppendTo[rr,i+s->I i];AppendTo[rr,i+2 s->-i];AppendTo[rr,i+3 s->-I i]],{i,s}];If[o>1,Print[{rr,s}]];gLoop=Table[gg[[i,j]]/.rr,{j,s},{i,s}];mm=Length[gLoop];If[indexTableQ[gLoop],If[r>0&&conservativeQ[gLoop]≠True,Print["Fail, non-conservative."];"TraditionalForm"[gLoop],gLoop],Print["Fail, not an indexTable."]];
id[gLoop];gLoop];

abbrFactors[g_,p_:power2]:=
Module[{ap,f,ff=fp[g,p],fi,fj,i=1,l,res={},temp},
f=If[NumberQ[First[ff]],Drop[ff,1],ff];f=If[NumberQ[First[f]],{Drop[f,1]},f];If[First[f]<0,f=-f];
While[i≤Length[f],fi=f[[i]];If[Length[f]===1,i++;fi=Exponent[f,"a"][[1]];fj=1;Goto[done]];
If[Head[f]===Power,i++;fj=Last[f];fi=If[Head[f[[-2,-1]]]===Power,f[[-2,-1,-1]],1];Goto[done]];
If[Head[f]===Plus&&(Head[f[[-1]]]===Power||Head[f[[-1]]]===Times),i=Length[f];fi=Exponent[f,"a"];fj=1;Goto[done]];
If[NumberQ[(fj=Last[fi])],fi=Last[Drop[fi,-1]],fj=1];
fi=Switch[Length[fi],0,1,1,1,2,Last[fi],_,Last[Last[fi]]];
Label[done];fi=fi/.{"ø"->1,"a"->1,-"a"->1,a->1};AppendTo[res,If[fj==1,ToString[fi],(((ToString[fi]))^(ToString[fj]))]];
i++];
temp=Union[res=Sort[Flatten[res]]];
Table[ap=temp[[i]];l=Length[Position[res,ap,1]];Which[Length[ap]>1&&l==1,((ap[[1]])^(ap[[2]])),Length[ap]>1,(Subscript[ap[[1]], 1]^(ap[[2]])),l==1,ap,True,(Subscript[ap, l])],{i,Length[temp]}]]

cosorbit[θ_,phaselist_:{0,1,2,3,4,5},scale_:1,meanlist_:Table[0,{24}]]:=Module[{m=Length[phaselist],i},Table[i=phaselist[[j]];meanlist[[j]]+If[NumberQ[i],scale*Cos[θ+2*Mod[i,m] π/m],0],{j,m}]]

proto[L_?indexTableQ,v_?VectorQ]:=Module[{oc=orderCount[L]},oc]

ω=2π/3;(* Used widely in orbits. Placed here to avoid evaluation in their definitions.*)

10.2 Generation by ca, co, sgroup.

ca[{m_,a_:1}]:=ca[m,a];ca[m_Integer?Positive]:=Table[Mod[i+j-2,m]+1,{i,m},{j,m}];
ca[m_Integer?Positive,a_Integer]:=Module[{k=Abs[a],test},test=If[GCD[m,k]==1,Table[Mod[i+If[EvenQ[i],j k-k+1,j]-2,m]+1,{i,m},{j,m}],Print[m," ",k," ","GCD not 1"];{},{}];If[a<0&&associativeQ[test,1]==False,Print["Not a group"];test,test,test]];

co[g_?indexTableQ,gg_?indexTableQ,hh_?indexTableQ,a_Integer,o_:0]:=co[g,co[gg,hh,a],o]
co[g_?indexTableQ,h_?indexTableQ,gg_?indexTableQ,hh_?indexTableQ,a_Integer,o_Integer:0,p_:0]:=co[g,co[h,co[gg,hh,a],o],p]
co[gg_?indexTableQ,hh_?indexTableQ,a_:0]:=
Module[{any,as=Abs[a],g1=Dimensions[gg][[1]],h1=Dimensions[hh][[1]],g=unsign[gg],h=unsign[hh],im,lm,test={},t,m},m=g1 h1;
If[Position[gg,Complex[_,_]]≠{},g=gg/.{any_/;Re[any]<0->-any+2g1,Complex[r_,i_]->If[i<0,-i+3g1,i+g1]}];If[Position[gg,𝕐]≠{},g=Mod[(gg/.{Times[𝕐 𝕐,any_]->any+2g1,Times[𝕐,any_]->any+g1,𝕐 𝕐->2g1+1,𝕐->g1+1})-1,3g1]+1];If[h≠hh,Print["Second matrix must not be signed"],If[as==7&&h≠C3,Print["Second matrix must be C3"],Do[lm=l-1;Do[t={};Do[
Do[Which[
as==0||as==1,AppendTo[t,(h[[k,l]]-1) g1+g[[i,j]]],
as<3,If[EvenQ[l]&&i>1,AppendTo[t,(h[[k,l]]-1) g1+g[[g1+2-i,j]]],AppendTo[t,(h[[k,l]]-1) g1+g[[i,j]]]],
as==3,If[EvenQ[j]&&k>1,AppendTo[t,Mod[(k+h[[k,l]]-2) g1+g[[i,j]]-1,m]+1],AppendTo[t,(h[[k,l]]-1) g1+g[[i,j]]]],
as==4,im=4 lm (i-1);If[EvenQ[l]&&EvenQ[i],AppendTo[t,(h[[k,l]]-1) g1+g[[Mod[i+im-1,g1]+1,j]]],AppendTo[t,(h[[k,l]]-1) g1+g[[i,j]]]],
as==7,If[lm==2,lm=3];im=lm (i-1);AppendTo[t,(h[[k,l]]-1) g1+g[[Mod[i+im-1,g1]+1,j]]],
True,Print[Unknown a];Abort[]],{i,g1}],{k,h1}];AppendTo[test,Mod[t-1,m]+1
  ],{j,g1}],{l,h1}]]];If[a<0||as==1,If[loopQ[test],If[associativeQ[test],test,Print["Not associative"];test],Print["Not a quasigroup"]],test,test]];

sgroup[m_?IntegerQ]:=Module[{e=Permutations[Range[m]],le,p},le=Length[e];
Table[p=Position[e,Apply[permute,{e[[i]],e[[j]]}]];
If[p==={},0,p[[1,1]]],{i,le},{j,le}]]

10.3 Functions centralizer, period, orderCount, etc.

centralizer[a_?IntegerQ,g_:gLoop]:=Module[{gg=If[Length[g]==1,g[[1]],g],b,c={}},Do[b=gg[[i,1]];If[gg[[a,i]]==gg[[i,a]],AppendTo[c,b]],{i,Length[gg]}];c]
period[g_:gLoop]:=Module[{gg=If[Length[g]==1,g[[1]],g],lg,a,aa,b,j,P={1}},lg=Length[gg];Do[a=gg[[i,1]];aa=a;j=2;While[(b=gg[[a,aa]])!=1&&j<lg,j++;aa=b];AppendTo[P,j],{i,2,lg}];P]
orderCount[g_:gLoop]:=Table[Length[Position[period[g],i]],{i,Max[Union[period[g]]]}]

center[g_:gLoop]:=centre[g];
centre[g_:gLoop]:=Module[{gg=If[Length[g]==1,g[[1]],g],lg,a,j,Z={}},lg=Length[gg];
Do[a=gg[[i,1]];j=1;While[gg[[a,j]]==gg[[j,a]]&&j<lg,j++];
If[j==lg,AppendTo[Z,a]],{i,lg}];Z]
gInverse[g_:gLoop]:=Module[{gg=If[Length[g]==1,g[[1]],g]},Flatten[Table[Position[gg[[i]],1],{i,Length[gg]}]]]

lcoset[h_,g_:gLoop]:=Module[{gg=gpd[g]},Intersection[Table[Union[Table[gg[[x,h[[j]]]],{j,Length[h]}]],{x,Length[gg]}]]]
rcoset[h_,g_:gLoop]:=Module[{gg=gpd[g]},Intersection[Table[Union[Table[gg[[h[[j]],x]],{j,Length[h]}]],{x,Length[gg]}]]]
normalSubgroup[h_,g_:gLoop]:=lcoset[h,g]==rcoset[h,g];
factorGroup[n_,g_:gLoop]:=Module[{gg=gpd[g],lc,loc,lg,lt},lg=Length[gg];If[(lc=lcoset[n,gg])≠rcoset[n,gg],Print[n," is not a Normal subgroup"],If[lg==Length[n],id[gg],lt=First[Transpose[lc]];loc=Table[Position[lc,i][[1,1]],{i,lg}];id[Table[loc[[gg[[lt[[i]],lt[[j]]]]]],{i,Length[lt]},{j,Length[lt]}]
]]]];

allFactorGroups[g_:gLoop,o_:0,i1_:2,i2_:49,p_:{}]:=Module[{a,b,f={},gg=gpd[g],i=If[p≠{},i1,i2],lc,lg,loc,lr,n,res,s},lg=Length[gg];If[o==0,s=subgroups[gg,0,i1,i]];s=sg;
Do[n=s[[k]];If[(lc=lcoset[n,gg])==rcoset[n,gg],res=First[Transpose[lc]];lr=Length[res];
loc=Table[Position[lc,i][[1,1]],{i,lg}];a=id[Table[loc[[gg[[res[[i]],res[[j]]]]]],{i,lr},{j,lr}]];
If[p≠{},If[MemberQ[p,b=gd[a][[2]]],f=b;Goto[tag]]]];
AppendTo[f,a],{k,Length[s]}];Label[tag];f]

10.4 Tests for Table Properties abelianQ etc.

abelianQ[gg_:gLoop]:=Module[{g=gpd[gg]},g===Transpose[g]]
associativeQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m},m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,
While[k≤m,If[Abs[g[[Abs[g[[i,j]]],k]]]≠Abs[g[[i,Abs[g[[j,k]]]]]],If[o===0,Throw[False],Throw[{False,i,j,k}]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]
AssociativeQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m},m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,
While[k≤m,If[g[[Abs[g[[i,j]]],k]]≠g[[i,Abs[g[[j,k]]]]],If[o===0,Throw[False],Throw[{False,i,j,k}]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

abelGrassmanQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m},m=Dimensions[g][[1]];a=abelianQ[g];
While[i≤m,While[j≤m,While[k≤m,If[Abs[g[[Abs[g[[i,j]]],k]]]≠Abs[g[[Abs[g[[k,j]]],i]]],If[o===0,Throw[False],Throw[{False,i,j,k}]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

alternativeQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,x,y,xy,x2,y2},m=Length[g];a=abelianQ[g];While[i≤m,x=Abs[g[[1,i]]];x2=Abs[g[[i,i]]];While[j≤m,
y=Abs[g[[1,j]]];xy=Abs[g[[i,j]]];If[Abs[g[[x,xy]]]≠Abs[g[[x2,y]]],If[o≠0,Throw[{False,i,j,k}],Throw[False],Throw[False]]];
If[Abs[g[[xy,y]]]≠Abs[g[[x,Abs[g[[y,y]]]]]],If[o≠0,Throw[{False,i,j,k,2}],Throw[False],Throw[False]]];
j++];i++;j=If[a,i,1]];
True]]

amQ[gg_:gLoop,o_:0]:=
Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,xy,yx,xz,zx},m=Length[g];
While[i≤m,
While[j≤m,xy=Abs[g[[i,j]]];yx=Abs[g[[j,i]]];
While[k≤m,xz=Abs[g[[i,k]]];zx=Abs[g[[k,i]]];If[g[[i,Abs[g[[yx,zx]]]]]≠g[[Abs[g[[xy,xz]]],i]],If[o===0,Throw[False],Throw[{False,i,j,k ," amQ"}]]];
k++];j++;k=1];i++;j=1];
True]]

bolQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,xz,yz,zx,zy},If[Position[g,Complex[_,_]]≠{},Throw["Complex"]];m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,
While[k≤m,xz=Abs[g[[i,k]]];yz=Abs[g[[j,k]]];zx=Abs[g[[k,i]]];zy=Abs[g[[k,j]]];If[Abs[g[[g[[k,yz]],i]]]≠Abs[g[[k,g[[Abs[g[[j,zx]]]]]]]],If[o===0,Throw[False],Throw[{False,i,j,k ," left Bol"}]]];If[Abs[g[[i,g[[zy,k]]]]]≠Abs[g[[Abs[g[[xz,j]]],k]]],If[o===0,Throw[False],Throw[{False,i,j,k ," right Bol"}]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

cQ[gg_:gLoop,o_:0]:=
Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,xy,yy},m=Length[g];
While[i≤m,
While[j≤m,xy=Abs[g[[i,j]]];yy=Abs[g[[j,j]]];
While[k≤m,If[g[[Abs[g[[xy,j]]],k]]≠g[[i,Abs[g[[yy,k]]]]],If[o===0,Throw[False],Throw[{False,i,j,k ," cQ"}]]];
k++];j++;k=1];i++;j=1];
True]]

conservativeQ[gg_:gLoop]:=Module[{A,B,da,db,dab,g=gpd[gg],m},m=Length[g];If[associativeQ[g]&&!signedTableQ[g],True,
A=Table[RandomReal[{-5,5}],{i,m}];da=Det[gmap[g,A]];B=Table[RandomReal[{-5,5}],{i,m}];db=Det[gmap[g,B]];AB=hoopTimes[A,B,g];dab=Det[gmap[g,AB]];A=Abs[da db-dab];B=Abs[da db+dab];Chop[((Min[A,B])/(Max[A,B]))]==0]]

entropicQ[gg_:gLoop,o_:0]:=Catch[Module[{g=gpd[gg],i=1,j=1,k=1,l=1,m=Length[g]},If[abelianQ[g],Throw[True]];While[i≤m,While[j≤m,
While[k≤m,
While[l≤m,If[Abs[g[[Abs[g[[i,j]]],Abs[g[[k,l]]]]]]≠Abs[g[[Abs[g[[i,k]]],Abs[g[[j,l]]]]]],If[o===0,Throw[False],Throw[{False,i,j,k,l}]]];
                l++];k++];l=1;j++;k=1];i++;j=1];
True]]

flexibleQ[gg_:gLoop,o_:0]:=Catch[Module[{i=1,j=1,k=1,g=gpd[gg],m},m=Length[g];
While[i≤m,(* Negated associators.  This is NOT as described in PMA p92 *)
While[j≤m,
While[k≤m,If[g[[Abs[g[[i,j]]],k]]-g[[i,Abs[g[[j,k]]]]]≠-g[[Abs[g[[k,j]]],i]]+g[[k,Abs[g[[j,i]]]]],If[o===0,Throw[False],Throw[{False,i,j,k,l}]]];
k++];j++;k=1];i++;j=1];
True]]

fenyvesQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,axy,zx,azx},m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,axy=Abs[g[[i,j]]];While[k≤m,zx=g[[k,i]];azx=Abs[zx];If[Abs[g[[i,Abs[g[[axy,k]]]]]]≠Abs[g[[i,Abs[g[[j,azx]]]]]],If[o≠0,Print[{g[[i,Abs[g[[axy,k]]]]],g[[i,Abs[g[[j,azx]]]]]}];Throw[{False,i,j,k}],Throw[False],Throw[False]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

flexQ[gg_:gLoop,o_:0]:=Catch[Module[{j=1,k=1,g=gpd[gg],m},m=Length[g];
While[j≤m,(* This is as described in PMA p92, with Abs *)
While[k≤m,If[Abs[g[[Abs[g[[k,j]]],k]]]===Abs[g[[k,Abs[g[[j,k]]]]]],,If[o===0,Throw[False],Throw[{False,j,k}]]];
k++];j++;k=1];
True]]

hamiltonianQ[g_:gLoop]:=Module[{s=subgroups[g]},!abelianQ[g]&&!MemberQ[Table[normalSubgroup[s[[i]]],{i,Length[s]}],False]];

indexTableQ[gg_:gLoop]:=Module[{g,i=2,l,r,c,t},If[gg≠{{}},g=Abs[gpd[gg]];r=If[Length[gg]==1,gg[[1,1]],gg[[1]]];t=Transpose[g];c=t[[1]];l=Length[g];If[r==c==Range[l],While[i≤l&&r==Union[Abs[g[[i]]]]==Union[Abs[t[[i]]]],i++]],l=i];i>l]

jordanQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j,k,g=gpd[gg],m,xx,axx,xy,axy},m=Length[g];a=abelianQ[g];
While[i≤m,xx=g[[i,i]];axx=Abs[xx];
While[j≤m,xy=g[[i,j]];axy=Abs[xy];If[Abs[g[[axy,axx]]]≠Abs[g[[i,Abs[g[[j,axx]]]]]],If[o≠0,Print[{g[[axy,axx]],g[[i,Abs[g[[j,axx]]]]]}];Throw[{False,i,j}],Throw[False],Throw[False]]];
j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

jacobiQ[gg_:gLoop,o_:0]:=Catch[Module[{g=gpd[gg],i=1,j,k,m=Length[g]},If[abelianQ[g],Throw[False]];
While[i≤m,
While[j≤m,If[g[[i,j]]≠-g[[j,i]],Throw[False]];While[k≤m,If[g[[i,g[[j,k]]]]+g[[j,g[[k,i]]]]+g[[k,g[[i,j]]]]≠0,If[o≠0,Print[{g[[i,g[[j,k]]]],g[[j,g[[k,i]]]],g[[k,g[[i,j]]]]}];Throw[{False,i,j,k}],Throw[False],Throw[False]]];
k++];j++;k=1];i++;j=1];
True]]

MoufangQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,axy,zx,azx,yz,ayz},m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,axy=Abs[g[[i,j]]];While[k≤m,zx=g[[k,i]];azx=Abs[zx];yz=g[[j,k]];ayz=Abs[yz];If[Sign[zx]Sign[yz]g[[azx,ayz]]≠g[[Abs[g[[k,axy]]],k]],If[o≠0,Print[{Sign[zx]Sign[yz]g[[azx,ayz]],g[[Abs[g[[k,axy]]],k]]}];Throw[{False,i,j,k}],Throw[False],Throw[False]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

moufangQ[gg_:gLoop,o_:0]:=Catch[Module[{a,i=1,j=1,k=1,g=gpd[gg],m,axy,zx,azx,yz,ayz},m=Length[g];a=abelianQ[g];
While[i≤m,
While[j≤m,axy=Abs[g[[i,j]]];While[k≤m,zx=g[[k,i]];azx=Abs[zx];yz=g[[j,k]];ayz=Abs[yz];If[Abs[g[[azx,ayz]]]≠Abs[g[[Abs[g[[k,axy]]],k]]],If[o≠0,Print[{g[[azx,ayz]],g[[Abs[g[[k,axy]]],k]]}];Throw[{False,i,j,k}],Throw[False],Throw[False]]];
k++];j++;k=If[a,j,1]];i++;j=If[a,i,1]];
True]]

negatableQ[gg_:gLoop,f_:2]:=Module[{g=gpd[gg],g1,s1,i,j,g2,l,m,t},
l=Length[g];m=Length[g]/f;If[!IntegerQ[m],False,g1=pick[g,{1,m},{1,m}];s1=Table[Sign[g1[[i,j]]],{i,m},{j,m}];
g1=g1/s1;g2=Table[Mod[g1+e m-1,l]+1*s1,{e,f}];j=0;Catch[While[i=0;
While[If[MemberQ[g2,pick[g,{m i+1,m i+m},{m j+1,m j+m}]],Null,Throw[False]];i++;i<f];j++;j<f];True]]]

loopQ[gg_:gLoop,O_:0]:=Catch[Module[{i=1,g=gpd[gg],Len,l,o,t},Len=Length[g[[1]]];l=Union[g[[1]]];t=Transpose[g];
  If[(Length[l]==Len)&&(Union[t[[1]]]==l),,If[O≠0,Print[{" First row, col incorrect",l,t[[1]]}]];Throw[False]];
  While[i≤Len,o=Complement[l,Abs[g[[i]]]];If[o≠{},If[O≠0,Print[{i," row missing",o}]];Throw[False]];
	o=Complement[l,Abs[t[[i]]]];If[o≠{},If[O≠0,Print[{ i," col missing",o}]];Throw[False]];
i++];True]]

signedTableQ[gg_:gLoop]:=If[(Union[gg[[1]]]≠Union[Flatten[gg]])&&indexTableQ[gg],True,False,False]

reductiveQ[gg_:gLoop,o_:0]:=Catch[Module[{g=gpd[gg],i=1,j=1,k=1,m=Length[g],xy,xx,yxx},If[MatrixQ[g],While[i≤m,xx=Abs[g[[i,i]]];
While[j≤m,xy=Abs[g[[i,j]]];yxx=Abs[g[[j,xx]]];(*Print[{i,j,xx,xy,g[[xy,xx]],g[[i,yxx]]}];*)
If[Abs[g[[xy,xx]]]==Abs[g[[Abs[g[[i,yxx]]]]]],Null,If[o===0,Throw[False],Throw[{False,i,j," reductiveQ"}]]];
j++;k=1];
i++;j=1],Throw[{False,g," not a matrix"}]];
True]]

riffQ[gg_:gLoop,o_:0]:=Catch[Module[{g=gpd[gg],i=1,j=1,k=1,m,xy,zxy,yz},m=Length[g];While[i≤m,
While[j≤m,xy=Abs[g[[i,j]]];While[k≤m,yz=Abs[g[[j,k]]];zxy=Abs[g[[k,xy]]];
If[Abs[g[[xy,zxy]]]==Abs[g[[Abs[g[[Abs[g[[i,yz]]],i]]],j]]],Null,If[o===0,Throw[False],Throw[{False,i,j,k," riffQ"}]]];
k++];
j++;k=1];
i++;j=1];
True]]

10.5 Operations reorder, gmap, lmatrix, rmatrix.

reorder[g_?indexTableQ,p_]:=Module[{gg,n,m,l=Length[p],o,gp},gg=gpd[g];n=Length[gg];gp=Abs[gg];m=Min[n,l];o=Join[p,Complement[Range[n],p]];(* Extend p to full size of g *)
o=Table[Position[o,i][[1,1]],{i,n}];
   Table[o[[gp[[p[[i]],p[[j]]]]]]Sign[gg[[p[[i]],p[[j]]]]],{i,m},{j,m}]]

gmap[g_:gLoop,v_]:=Module[{gg=g,l=Length[g]},Table[v[[Abs[gg[[i,j]]]]]Sign[gg[[i,j]]],{i,l},{j,l}]];
caylindex[g_]:=Module[{gg=gpd[g],e,j,l,n,s},l=Length[gg];n=Table[j,{j,1,l}];e=gg[[1]];s=Table[e[[j]]->n[[j]],{j,l,1,-1}];gg/.s];

gmap[g_:gLoop,v_]:=Module[{gg=gpd[g],m,i,st=1},If[MemberQ[Positive[gg],False,2],st=Table[Sign[gg[[i,j]]],{i,Length[gg]},{j,Length[gg]}];gg=Abs[gg]];m[i_]:=v[[i]];Map[m,gg,1]*st];
caylindex[g_]:=Module[{gg=gpd[g],e,j,l,n,s},l=Length[gg];n=Table[j,{j,1,l}];e=gg[[1]];s=Table[e[[j]]->n[[j]],{j,l,1,-1}];gg/.s];

lmatrix[]:=Module[{s,t},t=Table[0,{k,mm},{l,mm}];Do[Do[s=gLoop[[l,k]];t[[Abs[s],k]]=l Sign[s],{k,mm}],{l,mm}];t];
lmatrix[g_?indexTableQ]:=Module[{gg=gpd[g],m,s,t},m=Length[gg];t=Table[0,{k,m},{l,m}];Do[Do[s=gg[[l,k]];t[[Abs[s],k]]=l Sign[s],{k,m}],{l,m}];t];
rmatrix[]:=Module[{s,t},t=Table[0,{k,mm},{l,mm}];Do[Do[s=gLoop[[l,k]];t[[l,Abs[s]]]=l Sign[s],{k,mm}],{l,mm}];t];
rmatrix[g_?indexTableQ]:=Module[{gg=gpd[g],m,s,t},m=Length[gg];t=Table[0,{k,m},{l,m}];Do[Do[s=gg[[l,k]];t[[l,Abs[s]]]=k Sign[s],{k,m}],{l,m}];t];

10.6 Loops from Relators, ge; Monovectors,  Cayley-Dickson cd; Moufang doubling md.

smax=100;streprpt[str_,rul_,imax_:smax]:=Module[{s1=str,s2,ii=1},While[(s2=StringReplace[s1,rul])≠s1,ii++;If[ii>imax,If[imax==99,OK="Fail",Print[s1," ",s2," ","Failed. Increase smax?"];Abort[]]];s1=s2];s2]
matstrep[l_?MatrixQ,rul_,sm_:smax]:=Table[streprpt[l[[i,j]],rul,sm],{i,Dimensions[l,1][[1]]},{j,Dimensions[l,2][[1]]}]
ruleExpand[a___]:=Table[Rule[stringExpand[ToString[a[[i,1]]]],stringExpand[ToString[a[[i,2]]]]],{i,Length[a]}];

stringExpand[t_]:=Module[{e,f,g,l,n=1,res="",s=ToString[t]},If[s=="",res,l=StringLength[s];g=StringTake[s,1];res=res<>g;
While[g=StringTake[s,{n}];n++;n≤l,f=StringTake[s,{n}];
e=ToExpression[f];If[IntegerQ[e],If[n<l&&IntegerQ[ToExpression[StringTake[s,{n+1}]]],e=ToExpression[StringTake[s,{n,n+1}]];n++;];
Do[res=res<>g,{i,e-1}],res=res<>f]]];
res];Attributes[stringExpand]={Listable,Protected};

ge[gp0_,pre_:{},o_:0,f_:0]:=Module[{gpa=Flatten[Abs[gp0]],g={},g0=Flatten[gp0],cr,j,l,le,ln=1,lh,lhs,n={""},new,p,q,st,rhs,t=ruleExpand[pre],si,sij},l=IntegerPart[Plus@@gpa]+2;le=Length[gpa];cr=Take[{"𝕒","𝕓","𝕔","𝕕","𝕖","𝕗","𝕘"},le];

(*Add 𝕒2->-1 rules*)q=Position[gp0,-2];
Do[j=cr[[q[[i,2]]]];AppendTo[t,Rule[j<>j,cr[[-1]]]],{i,Length[q]}];

(*Add 𝕓𝕒->𝕒𝕓𝕔 rules*)q=gp0[[1]];
If[ListQ[q],
Do[j=cr[[i]];Do[AppendTo[t,Rule[cr[[k]]<>j,j<>cr[[k]]<>cr[[-1]]]],{k,i+1,Length[q]}],
{i,Length[q]}]];

Catch[(*Reject bad rules.*)If[o≠0,Do[(*i loop,Relators*)Do[(*r loop,each rule*)Do[(*k loop,lhs & rhs*)If[(rhs=Characters[t[[r,2]]])≠Sort[rhs]||((lhs=Characters[t[[r,1]]])==Sort[lhs]&&Length[Union[lhs]]>1),Print[{"Bad order",t[[r]]}];Throw[Null]];
If[Length[Complement[Union[lhs,rhs],cr]]>0,Print[{"Unknown Relator ",t[[r]],cr}];Throw[Null]];
j=Length[Position[Characters[t[[r,k]]],cr[[i]]]];If[GCD[j,IntegerPart[gpa[[i]]]]>1&&j≠0&&j≠IntegerPart[gpa[[i]]],Print[{"Bad GCD ",j,gpa[[i]],t[[r]]}];Throw[Null]],{k,2}],{r,Length[t]}],{i,Length[gpa]}]];strep={};

Do[(*i loop. Add the rules to reduce repetitions*)st=cr[[i]];AppendTo[t,Do[st=st<>cr[[i]],{IntegerPart[gpa[[i]]]-1}];Rule[st,""]],{i,le}];
Do[(*i,j loops. Add abelianQ rules*)new=Rule[lh=cr[[j]]<>cr[[i]],cr[[i]]<>cr[[j]]];Do[(*k loop, redundant rules*)If[lh==t[[k,1]],new=""],{k,Length[t]-1}];If[Length[new]==2,AppendTo[t,new]],{i,1,le},{j,i+1,le}];
Do[(*i loop,symbols. Build the element list*)si=cr[[i]];sij=si;p=IntegerPart[gpa[[i]]]-1;
Do[(*j loop.Repetitions*)
Do[(*k loop,new element=j repeats of k'th existing element*)
AppendTo[n,If[k==1,sij,n[[k]]<>sij]],{k,ln}];sij=sij<>si,{j,p}];ln=Length[n],{i,le}];(*element list completed*)

Do[AppendTo[g,(*add successive n[[i]]<>n rows to g*)MapThread[StringJoin,{Table[n[[i]],{j,ln}],n}]],{i,ln}];
g=matstrep[g,t];
If[o==0,gel=.;matel=.;strep=.,
gel=n/.""->ø;matel=g/.""->ø];
g=caylindex[g];

(*Convert to a signed table?*)
If[Head[Last[gp0]]==List,g=ts[g,gp0[[-1,1]]]];
If[f≠{},ln=1;Do[If[le>=i&&!IntegerQ[(l=gpa[[f[[i]]]])],ln*=l],{i,Length[f]}];
ln=IntegerPart[Abs[ln]];le=Length[g]/ln;g=ts[g,ln]
];

If[o≠0,gel=ToExpression[Take[gel,le]];matel=ToExpression[Transpose[Take[Transpose[Take[matel,le]],le]]]];

(*Report properties?*)
If[Abs[o]≠0,If[loopQ[g],If[associativeQ[g,1],g,Print["Non-associative"];g],Print["Not a quasigroup"]]];
gLoop=g]];

cd[{g_String}]:=ToExpression[g];cd[{}]:={{1}};cd[{2}]:={{1,2},{2,3}};cd[{-2}]:={{1,2},{2,-3}};cd[{2.}]:={{1,2},{2,-1}};cd[{3}]:={{1,2,3},{2,3,1},{3,1,2}}(*C3*);cd[{3.}]:={{1,2,3},{2,3,-1},{3,-1,-2}};cd[{-3}]:={{1,2,3},{2,-3,1},{3,1,-2}};cd[{4}]:={{1,2,3,4},{2,3,4,1},{3,4,1,2},{4,1,2,3}}(*C4*);
cd[{4.}]:={{1,2,3,4},{2,1,-4,-3},{3,-4,1,-2},{4,-3,-2,1}};
cd[{gamma__}]:=
Module[{l=Last[{gamma}],n,q,r,(*Recursion*)m=cd[Drop[{gamma},-1]]},
q=Length[m];n=IntegerPart[l];
Which[ListQ[l],co[m,ca[l]](*compose with group*),
StringQ[l],
co[m,ToExpression[l]]           (*compose with hoop*),
True                                                    (* new relator*),
Table[Which[i≤q&&j≤q,m[[i,j]](* Top-left *),
i≤q,modqr[q,m[[j-q,i]]]          (* Top-right *),
j≤q,r=m[[i-q,j]];                     (* Bottom left*)
Which[ !IntegerQ[l],modqr[q,r](* simple, real l *),
j≠1,n modqr[q,r]       (* negate all but col 1 *),
True,q+Abs[r]]            (* shift by default*) ,
True,r=m[[j-q,i-q]]      (* Bottom-right i,j>q*);
If[IntegerQ[l]&&j≠q+1&&q>1, r,
n r(* negate all but col 1 if l negative real*)]],
{i,2q},{j,2q}(*Table indices*)]]]
modqr[q_,r_]:=(Mod[(q+Abs[r])-1,2q]+1)Sign[r]

md[g_?MatrixQ,l_:{}](*From Loop in GAP*):=
Module[{m=Length[g],gin=If[l=={},gInverse[g],l]},
res=Table[0,{i,2m},{j,2m}];Do[Do[res[[i,j]]=g[[i,j]](* Top-left g *);
res[[i,j+m]]=g[[j,i]]+m(* Top-right (g^T)+m*);
res[[i+m,j]]=g[[i,gin[[j]]]]+m(* Bottom left g+m reordered*);
res[[i+m,j+m]]=g[[gin[[j]],i]](* Bottom right (g^T) reordered*),
{i,m}],{j,m}];res];

10.7 Groups from Permutations, pe & PermutationGroup.

Mathematica 8 has an extensive suite of functions that render this obsolete.

pe[pcl_,maxel_:80]:=Module[{m,g={Range[Max[Flatten[pcl]]]},i,j,k,n,o={}},permel={};If[Depth[pcl]<3,Print[pcl,"is not a list of permutations or cycles"];Abort[]];If[MemberQ[pcl,g[[1]]],Print[g[[1]]," unacceptable"];Abort[]];
Do[j=pcl[[i]];k=If[VectorQ[j],j,fromCycles[j]];AppendTo[g,k],{i,Length[pcl]}];
j=2;k=1;While[j≤Length[g],k++;n=permute[g[[j]],g[[k]]];If[!(MemberQ[g,n]),AppendTo[g,n]];If[k≥Length[g],k=1;j++;If[j>maxel+1,Print["Large"];i=l+1;j=l+1;i=0;pcl=0;nn=0;Goto[tag]]]];permel=g;o=caylindex[Table[permute[g[[i]],g[[j]]],{i,Length[g]},{j,Length[g]}]];Label[tag];gLoop=o]

The 10th entry in loop is the Cycles data for the non-PC groups A5, S5, SL24, SL25. It is accessed as follows:-

{pg=PermutationGroup[Map[Cycles,ToExpression[loop[[120,2,10]]],{1}]],
GroupOrder[pg],
id[gapLoop=GroupMultiplicationTable[pg]]}

10.8 MatrixGroups using extended signs, ma, mg, ms, msi.

ma[{mM__?MatrixQ},maxel_:81,o_:0]:=Module[{g,j=2,k=1,m={mM},mx=2,newM},findROU[m,1];g=union[{IdentityMatrix[Length[m[[1]]]],mM}];
While[j≤Length[g],k++;newM=Simplify[Expand[g[[j]].g[[k]]]/.rofu];
If[!(MemberQ[g,newM]),AppendTo[g,newM];mx++;If[mx>maxel,k=9999;j=mx]];If[k≥Length[g],k=1;j++;If[j>maxel,matel={};g={{}};Goto[tag]];
]](*EndWhile*);matel=g;
If[o==0,g=caylindex[
Table[Simplify[Expand[g[[i]].g[[j]]]/.rofu],{i,Length[g]},{j,Length[g]}]];
gLoop=g];
Label[tag];g]

mg[v_?VectorQ,u_:u2,maxel_:81]:=Module[{},ma[Table[u[[Abs[v[[i]]]]]Sign[v[[i]]],{i,Length[v]}],maxel]]

ms[v__?ListQ,u_:u2,maxel_:81]:=(*Signed loop from UMM matrices*)
Module[{gg,gij,i=2,j=2,l,new,n,p,s,tot=0,m=If[VectorQ[v],Table[Sign[v[[i]]]u[[Abs[v[[i]]]]],{i,Length[v]}],v]},
findROU[m,1];(*sets rofu to eliminate high powers*)
s=Union[{1,-1},Variables[m]];(* admissible signs *)
If[MatrixQ[m[[1]]]===True,Null,Print[ "Not a list or matrix"];gg={{}};Return[]];
l=Length[m[[1]]];n=Length[m]+1;matel=Prepend[m,IdentityMatrix[l]];
While[(*i*)j=2;
While[(*j*)new=Simplify[Expand[matel[[i]].matel[[j]]]/.rofu];
If[mstst[new,s]==0,AppendTo[matel,new]];tot++;If[Length[matel]>maxel||tot>4 maxel,Print[{new,"Too long.",tot}];gg={{}};Abort[]];
j<Length[matel],j++];
i<Length[matel],i++];
n=Length[matel];gg=Table[Simplify[Expand[matel[[i]].matel[[j]]]/.rofu],{i,n},{j,n}];
Do[gij=gg[[i,j]];p=mstst[gij,s];gg[[i,j]]=p Position[matel,p gij][[1,1]],{i,n},{j,n}];gLoop=.;If[indexTableQ[gg]==True,gLoop=gg];gLoop]
mstst[m_,s_]:=Module[{i=0,l=Length[s],res=0},While[i<l,i++;If[Position[matel,s[[i]]m]=={},,res=s[[i]];i=l]];res];
msi[v__?ListQ,u_:u2,si_:{1,-1,I,-I},maxel_:81]:=(*ms for P4, P16c*)
Module[{gg,gij,i=2,j=2,l,mi,new,n,p,s,tot=0,m=If[VectorQ[v],Table[Sign[v[[i]]]u[[Abs[v[[i]]]]],{i,Length[v]}],v]},
findROU[Flatten[m],1];s=Union[si,Variables[m]];
If[MatrixQ[m[[1]]]===True,,Print[ "Not a list or matrix"];Abort[]];
l=Length[m[[1]]];n=Length[m]+1;matel=Prepend[m,IdentityMatrix[l]];
While[j=2;
While[new=Simplify[Expand[matel[[i]].matel[[j]]]/.rofu];
If[mstst[new,s]==0,AppendTo[matel,new]];tot++;If[Length[matel]>maxel||tot>4 maxel,Print[matel];Abort[]];
j<Length[matel],j++];i<Length[matel],i++];
n=Length[matel];gg=Table[Simplify[Expand[matel[[i]].matel[[j]]]/.rofu],{i,n},{j,n}];
Do[gij=gg[[i,j]];p=mstst[gij,s];gg[[i,j]]=p Position[matel,p gij][[1,1]],{i,n},{j,n}];gLoop=.;If[indexTableQ[gg]==True,gLoop=gg];gLoop]

10.9 Protoloops; makeProtoloop[G_,o_],  mp, gd.

mp[]:=makeProtoloop[{mm,nn},0];
mp[m_?IntegerQ,n_?IntegerQ]:=makeProtoloop[{m,n},0];
mp[{a_,b_},o_?IntegerQ]:=makeProtoloop[{a,b},o];
mp[m_?IntegerQ,n_?IntegerQ,o_?IntegerQ]:=makeProtoloop[{m,n},o];
mp[a_]:=makeProtoloop[a,0];
makeProtoloop[m_?IntegerQ,n_?IntegerQ,o_?IntegerQ]:=makeProtoloop[{m,n},o];
makeProtoloop[m_?IntegerQ,n_?IntegerQ]:=makeProtoloop[{m,n},0];
makeProtoloop[G_]:=makeProtoloop[G,0];
makeProtoloop[G_,o_?IntegerQ]:=Module[{g,l,res,mx=mg},matel=.;If[Head[G]===Symbol,Print[{G,"not a known Table. Changed to a string."}];G=ToString[G]];
Which[
MatrixQ[G],id[caylindex[G]],
Head[G]===String,g=Position[loop,G,3,1];
  If[g==={},Print[{"Unknown case ",o," ",G}];Abort[]],
  (* mm=g[[1,1]];nn=g[[1,2]],*)
Length[G]===2,If[Length[loop[[G[[1]]]]]≥G[[2]],mm=G[[1]];nn=G[[2]],Return[{"Unknown mm,nn ",G}] ],
True,mm=Length[loop];Return[{"Unknown ",G}]];(*End Which*)
If[Sign[loop[[mm,nn]][[2,1]]]≠1,mx=ms];(*Signed*)
If[mm≥Length[loop]||(l=loop[[mm]])=={}||Length[l]<nn,gName="Unrecognized",l=l[[nn]];gName=loop[[mm,nn,1]]];res=Which[o<1&&l[[4]]!="ca[]",ToExpression[l[[4]]],
(o==0||o==1)&&l[[5]]≠{},ge[l[[5]],l[[6]],0,0],
(o==0||o==2)&&Length[l]>6&&l[[7]]≠{},mx[l[[7]],u2],
(o==0||o==3)&&Length[l]>7&&l[[8]]≠{},mx[l[[8]],u3],
(o==0||o==4)&&Length[l]>8&&l[[9]]≠{},mx[l[[9]],u4],
(o==0||o==5)&&Length[l]>9&&ListQ[l[[10]]],pe[l[[10]]],
(o==0||o==5)&&Length[l]>9,ToExpression[l[[10]]],
(o==0||o==6)&&Length[l]>10,ToExpression[l[[11]]],
True,Print[{G,"No Protoloop",o}];{}];id[res];gLoop=res];

gd[]:=gd[mm,nn];gd[{m_Integer,n_Integer}]:=gd[m,n];gd[m_Integer:mm,n_Integer:nn]:=If[m≥Length[loop]||m>0&&loop[[m]]≠{}&&n>0&&Length[loop[[m]]]≥n,{mm=m,nn=n,loop[[m,n]]},"Not a loop index"];
gd[g_]:=Module[{i},Which[
Head[g]===String&&(i=Position[loop,g,3,1])≠{},gd[mm=i[[1,1]],nn=i[[1,2]]],
Head[g]===String&&(i=Position[loop,g<>"?",3,1])≠{},gd[mm=i[[1,1]],nn=i[[1,2]]],
True,Print["Not a loop index or known mnemonic. Try as a string?"]]]

10.10 Loop identification id, idc.

idc[G_]:=If[conservativeQ[G],id[G],"Not conservative."];
idc[G_,L_?ListQ]:=If[conservativeQ[G],id[G,L],"Not conservative."];id[{{1}}]:=gName="C1";Return[gName];
id[]:=id[{mm,nn},{}];
id[G_:{mm,nn}]:=id[G,{}];id[G_:{mm,nn},L_?ListQ]:=Module[{ln,lg,j,jj,M,res=""},nn=1;If[Head[G]===TraditionalForm,M=G[[1]],M=G];
If[Head[G]===String,M=mp[G]];Which[Dimensions[M]=={2},mm=M[[1]];nn=M[[2]];M={},
MatrixQ[M],M=If[Length[L]>0,reorder[M,L],M];mm=Length[M],
True,mm=Length[loop];gLoop=.;M={}];
lg=Length[M];
If[lg>1&&(j=Position[loop[[lg]][[All,{2}]],dico[M],3,1])≠{},nn=j[[1,1]],mm=Length[loop]];
jj=loop[[mm,nn,3]];ln=nn;
Switch[jj,0,,
1,Switch[trico[M],{3,(Subscript[3, 2])},"C9",{9},nn++;"C3C3",{6,3},nn+=4;"Alt9n"],
2,If[Length[fa[M]]==2,"Dav",nn+=3;"C4C2r"],
3,If[subgroups[M,0]==9,nn+=3;"C8C2","C4C4"],
4,If[subgroups[M,0,5,5]≠1,"C3C25",nn++;"C75"],
5,If[trico[M]==={3,(Subscript[3, 5])},"C18",nn+=3;"C3C3C2"],
6,If[trico[M]==={9,(Subscript[1, 9])},nn+=3;"E18","D9"],
7,If[Length[fa[M]]==2,"C3KJ",nn+=5;"C4C3j"],
8,Switch[trico[M],{3,(Subscript[3, 8])},"C27",{9,(Subscript[9, 2])},nn++;"C9C3",{27},nn+=4;"C3C3C3"],
9,If[subgroups[M,0]==1,"C25",nn++;"C5C5"],
10,Switch[trico[M],{9,(Subscript[9, 2])},nn++;"g2704",{27},"P27"],
11,Switch[subgroups[M,0,0,8],33,nn+=31;"g3233",37,nn+=22;"g3224",any_,"g3202"],
12,If[conservativeQ[M],"C4C4r",nn+=2;"C4Kcn"],
13,If[trico[M]==={1,(Subscript[1, 13]),2},"CL31",nn++;"CL22"],
14,If[Length[centre[M]]==8,"KiC8",nn+=6;"g3211"],
15,If[trico[M]==={1,(Subscript[1, 11]),(Subscript[2, 2])},"CL4",nn+=3;"CL13"],
17,If[Length[centre[M]]==8,"C4iC4C2",nn+=6;"KiQ8"],
18,Switch[Max[First[Transpose[collect[subgroupTypes[subgroups[M,1,16,16]]]]]],2,mm=32;nn=25;"D4C4",3,mm=32;nn=30;"G3230",4,mm=32;nn=31;"g3231"],
19,If[Length[centre[M]]==4,nn+=6;"Q8C4a","g3226"],
20,If[conservativeQ[M],"QC2c",nn+=19;"QC2cn"],21,If[Length[centre[M]]==4,"g64091";mm=64;nn=ln+13,"g64078";mm=64;nn=ln],
22,If[Position[M,-I]==={},nn++;"C3i","C12c"],
23,If[subgroups[M,0,3,3]==1,"C36",nn+=6;"C12C3"],
24,If[subgroups[M,0,3,3]==1,"C18C2",nn+=9;"C6C6"],
25,If[subgroups[M,0,3,3]==1,"D18",nn+=9;"E18C2"],
26,If[subgroups[M,0,3,3]==1,"Q36",nn+=6;"C3iQ12"],
27,If[subgroups[M,0,3,3]==1,"g3603",nn+=8;"A4C3"],
28,Switch[allFactorGroups[M,0,2,2,{37,38}],37,"g64104";mm=64;nn=ln,38,"g64105";mm=64;nn=ln+1],
29,Switch[trico[M],{3,(Subscript[3, 20])},"C63",{9,(Subscript[9, 6])},nn+=2;"C7C3C3"],
30,If[subgroups[M,0,3,3]==1,"C45",nn++;"C5C3C3"],
32,If[subgroups[M,0,4,4]==7,"C3C4C4",nn+=3;"C24C2"],
33,If[Length[centre[M]]==4,nn++;"g4805","C8D3"],
34,Switch[subgroups[M,0,32,0,{3,7,11,15,36,38,42}],
36,"g64116";mm=64;nn=116,
3,"g64117";mm=64;nn=117,
7,"g64117";mm=64;nn=117,
_,"g64124";mm=64;nn=124],
35,If[subgroups[M,0,4,4]==15,nn+=2;"C4D6","P48"],
36,If[subgroups[M,0,4,4]==3,If[Length[centre[M]]≠4,"C24g17C2",nn++;"g4810"],nn+=2;"Q12C4"],
37,Switch[subgroups[M,0,4,4],11,"A4C4",7,nn+=2;"g4833"],
38,If[subgrpPerm[M,0,7,7]==1,"C49",nn++;"C7C7"],
39,If[subgrpPerm[M,0,5,5]==1,"C50",nn+=3;"C10C5"],
40,If[subgrpPerm[M,0,5,5]==1,"D50",nn+=3;"C5iD10"],
41,If[subgrpPerm[M,0,9,9]==4,"P54",nn+=5;"E18nC3"],
43,Switch[trico[M],{3,(Subscript[1, 27]),(Subscript[3, 8])},D54,_,nn+=13;"D27b"],
44,Switch[allFactorGroups[M,0,2,2,{39,40}],39,"g64118";mm=64;nn=ln,40,"g64119";mm=64;nn=ln+1],
45,If[trico[M]==={9,(Subscript[3, 9]),(Subscript[9, 2])},"C9D3",nn+=8;"D3C3C3"],
46,If[MemberQ[allFactorGroups[M,0,2,2],"g3215"],"g64022";mm=64;nn=ln+3,mm=64;nn=ln;"g64019"],
47,If[MemberQ[allFactorGroups[M,0,2,2],"D8iC4"],"g64013";mm=64;nn=ln,mm=64;nn=ln+1;"g64014"],
48,If[subgroups[M,0,4,4]==27,"g64020",nn+=2;"g64022"],
49,Switch[subgroups[M,0,8,8],7,"g64026",nn+=24,"g64050"],
50,Switch[allFactorGroups[M,0,2,2,{16,17}],
17,"g64027";mm=64;nn=ln,16,"g64051";mm=64;nn=ln+24],
51,If[MemberQ[allFactorGroups[M,0,2,2],"g3211"],"g64020";mm=64;nn=ln+2,mm=64;nn=ln;"g64018"],
52,Switch[allFactorGroups[M,0,2,2,{2,9,14,40,42}],
40,"g64106";mm=64;nn=ln+85,
42,"g64108";mm=64;nn=ln+87,
_,"g64021";mm=64;nn=ln],
53,If[subgroups[M,0,4,4]==31,"g64135","g64136";nn++],
54,If[Length[centre[M]]==4,"g64177";nn+=43,If[subgroups[M,0,4,4]==35,"g64190";nn+=56,"g64134"]],
55,Switch[subgroups[M,0,32,0,{16,17}],16,nn=ln;"g64044",17,nn=ln+1;"g64045"],
56,Switch[subgroups[M,0,16,16],19,"g64057";nn=ln,11,"g64064";nn=ln+7,7,"g64082";nn=ln+25],
57,Switch[allFactorGroups[M,0,2,2,{31,42}],
31,"g64167";mm=64;nn=ln,42,"g64176";mm=64;nn=ln+9,_,"g64173";mm=64;nn=ln+6],
58,Switch[allFactorGroups[M,0,2,2,{22,43,28}],22,"g64100";mm=64;nn=ln,43,"g64109";mm=64;nn=ln+9,28,"g64151";mm=64;nn=ln+51],
59,Switch[allFactorGroups[M,0,2,2,{11,28,37,38,42}],
37,"g64088";mm=64;nn=ln,
38,"g64089";mm=64;nn=ln+1,
42,"g64097";mm=64;nn=ln+9,
11,"g64101";mm=64;nn=ln+13,
28,"g64152";mm=64;nn=ln+64],
60,Switch[allFactorGroups[M,0,2,2,{5,4,17,24}],
5,"g64017";mm=64;nn=ln,
4,"g64084";mm=64;nn=ln+67,
17,"g64184";mm=64;nn=ln+167,
24,"g64112";mm=64;nn=ln+95,
_,Switch[allFactorGroups[M,0,2,2,{36,37,38}],
36,"g64185";mm=64;nn=ln+168,
37,"g64085";mm=64;nn=ln+68,
38,"g64086";mm=64;nn=ln+69]],
61,Switch[allFactorGroups[M,0,2,2,{16,36}],36,"g64083";mm=64;nn=ln,16,"g64183";mm=64;nn=ln+100],
62,Switch[allFactorGroups[M,0,2,2,{37,38}],37,"g64113";mm=64;nn=ln,38,"g64114";mm=64;nn=ln+1],
63,Switch[allFactorGroups[M,0,2,2,{31,34}],31,"g64074";mm=64;nn=ln,34,"g64080";mm=64;nn=ln+6],
64,Switch[allFactorGroups[M,0,2,2,{31,32}],31,"g64071";mm=64;nn=ln+4,_,"g64067";mm=64;nn=ln],
65,Switch[allFactorGroups[M,0,2,2,{23,25,26,28}],26,"g64072";mm=64;nn=ln+2,_,"g64070";mm=64;nn=ln],
66,Switch[allFactorGroups[M,0,2,2,{25,26,30,31,33}],
31,"g64063";mm=64;nn=ln,
_,"g64068";mm=64;nn=ln+5],
67,Switch[allFactorGroups[M,0,2,2,{22,31}],
22,"g64062";mm=64;nn=ln,
_,"g64069";mm=64;nn=ln+7],
69,Switch[allFactorGroups[M,0,2,2,{2,24}],
2,"g64056";mm=64;nn=ln,
24,"g64195";mm=64;nn=ln+139,
_,"g64198";mm=64;nn=ln+142],
70,Switch[allFactorGroups[M,0,2,2,{40,42}],
40,"g64129";mm=64;nn=ln,
42,"g64133";mm=64;nn=ln+4,
_,"g64161";mm=64;nn=ln+32],
71,Switch[allFactorGroups[M,0,2,2,{40,42}],
42,"g64130";mm=64;nn=ln,
40,"g64131";mm=64;nn=ln+1],
72,If[conservativeQ[M],"C3C2",nn+=12;"C6an"],73,If[Length[centre[M]]==4,"g64178";nn+=41,"g64137"],
74,Switch[collect[allFactorGroups[M,0,8,8,{16,16}]][[1,1]],
15,"g64159";mm=64;nn=ln+17,
23,"g64157";mm=64;nn=ln+15,
25,"g64145";mm=64;nn=ln+3,
_,"g64142";mm=64;nn=ln],
75,Switch[allFactorGroups[M,0,2,2,{40,42}],40,"Q8pQ8";mm=64;nn=ln,42,"g64160";mm=64;nn=ln+4],
76,Switch[allFactorGroups[M,0,2,2,{40,42}],40,"g54162";mm=64;nn=ln,42,"g64163";mm=64;nn=ln+1],
77,Switch[allFactorGroups[M,0,2,2,{40,42}],40,"g54164";mm=64;nn=ln,42,"g64166";mm=64;nn=ln+2],
78,Switch[allFactorGroups[M,0,2,2,{31,42}],31,"g54168";mm=64;nn=ln,42,"g64180";mm=64;nn=ln+12,_,"g64179";mm=64;nn=ln+11],
79,Switch[allFactorGroups[M,0,2,2,{18,34}],18,"g54186";mm=64;nn=ln+12,34,"g64174";mm=64;nn=ln],
81,Switch[allFactorGroups[M,0,2,2,{19}],19,"g64187";mm=64;nn=ln,_,"g64189";mm=64;nn=ln+2],
82,Switch[allFactorGroups[M,0,2,2,{27,34,39}],27,"g64202";mm=64;nn=ln,34,"g64211";mm=64;nn=ln+9,39,"g64250";mm=64;nn=ln+48],
83,Switch[collect[allFactorGroups[M,0,8,8,{16,16}]][[1,1]],
10,"g64206";mm=64;nn=ln+1,
6,"g64207";mm=64;nn=ln+2,
11,"g64213";mm=64;nn=ln+8,
_,"g64205";mm=64;nn=ln],
84,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==21,"g64208";mm=64;nn=ln,"g64214";mm=64;nn=ln+6],
85,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==105,"g64215";mm=64;nn=ln,"g64216";mm=64;nn=ln+1],
86,Switch[collect[allFactorGroups[M,0,4,4]][[1,1]],38,"g64227";mm=64;nn=ln,49,"g64227";mm=64;nn=ln,_,"g64231";mm=64;nn=ln+4],
87,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==63,"g64219";mm=64;nn=ln,"g64221";mm=64;nn=ln+2],
88,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==36,"g64228";mm=64;nn=ln,"g64229";mm=64;nn=ln+1],
89,Switch[collect[allFactorGroups[M,0,4,4]][[1,1]],58,"g64232";mm=64;nn=ln,44,"g64240";mm=64;nn=ln+8,42,"g64234?36";mm=64;nn=ln+2],
90,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==71,"g64241";mm=64;nn=ln,"g64242";mm=64;nn=ln+1],
91,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==32,"g64247";mm=64;nn=ln,"g64248";mm=64;nn=ln+1],
92,If[collect[allFactorGroups[M,0,4,4]][[1,1]]==45,"g64251";mm=64;nn=ln,"g64253";mm=64;nn=ln+2],
93,If[Length[centre[M]]==4,"g64254";mm=64;nn=ln,"g64257";mm=64;nn=ln+3],
94,If[Length[centre[M]]==4,"g64256";mm=64;nn=ln,"g64258";mm=64;nn=ln+2],
95,If[Length[centre[M]]==4,"g64255";mm=64;nn=ln,"g64259";mm=64;nn=ln+4],
96,If[Length[centre[M]]==4,"g64???";mm=64;nn=ln,"g64???";mm=64;nn=ln+4],
97,If[Length[fp[M,el2]]==6,nn+=17;"O4k","O4"],
98,If[!conservativeQ[M],nn++;"D4M4n","Q8M"],
99,If[!associativeQ[M],nn+=23;"C8pC2M","g3238"],
100,Switch[collect[allFactorGroups[M,0,4,4]][[1,1]],19,"g64146";mm=64;nn=ln+52,22,"g64102";mm=64;nn=ln+8,_,"g6494";mm=64;nn=ln]
];(*mm, nn, and res found. Restore gLoop *)gLoop=M;
If[mm>Length[loop]||nn>Length[loop[[mm]]],gName="Unknown",
gName=loop[[mm,nn,1]]]];

10.11 Subgroup Routines subgroups, subgroupTypes, collect, dic, dico, etc

subgroups[G_?MatrixQ,o_:0,i1_:2,i2_:49,pp_:associativeQ]:=Module[{d,divs,dl,f=-1,g,i,j,l=Length[G],n=0,p=pp,r,test=0,v=Drop[G[[1]],1]},
If[i1≠2&&GCD[l,i1]==1,Print[i1," is not a factor of ",l]; Abort[]];i=If[NumberQ[i2],Max[i1,i2],i1];
Which[o<0, test={-o};i=i1,p=={},p=associativeQ,ListQ[p],test=p];
divs=Select[Drop[Drop[Divisors[l],-1],1]-1,i>#1>=i1-1&];sg={};
gLTop=G;(* Now find all potential subloops in the range *)
d=Flatten[Table[KS[v,divs[[i]]],{i,Length[divs]}],1];dl=Length[d];If[o>2,Print[{dl," cases"}];];
j=0;While[j++;j<dl,r=Flatten[{1,d[[j]]}];
If[select[r]==r,(* quasi-group filter *)g=reorder[G,r];
Which[
ListQ[test],If[associativeQ[g]&&(f=id[g])≠"Unrecognised"&&MemberQ[test,f=gd[][[2]]],Goto[tag],gLTop=G;f=0],
p[g],n++;AppendTo[sg,r]]
]];Label[tag];
Which[f>-1,f,(* target found? *)
o==0,n, (* count  *)
o==1,sg,(* subloop list *)
True,Print[" Number of subloops = ",n];sg]];

KS[l_List,1,gap_:{},lef_:{}]:=Partition[l,1]
KS[l_List,k_Integer?Positive,gap_:{},lef_:{}]:={l}/;(k==Length[l])
KS[l_List,k_Integer?Positive,gap_:{},lef_:{}]:=Module[{f=First[l],g,ngap,nlf},
nlf=Append[lef,f];ngap=Append[gap,f];g=Length[Intersection[select[nlf],gap]];If[g>0,KS[Drop[l,1],k,ngap,lef],
Join[Map[(Prepend[#,f])&,KS[Drop[l,1],k-1,gap,nlf]],KS[Drop[l,1],k,ngap,lef]]]]

dic[g_:gapLoop]:=Module[{c=0,d,
gf=Sign[Flatten[g]],j,k,n=Table[g[[i,i]],{i,Length[g]}],o=If[g==Transpose[g],1.,1]},If[MemberQ[gf,I]||MemberQ[gf,-I],o=I o];If[MemberQ[gf,𝕐]||MemberQ[gf,(𝕐^2)],o=𝕐 o];
Do[j=k=g[[i,i]];While[(k=g[[Abs[j],Abs[k]]])≠Abs[j]&&c<9999,c++],{i,Length[g]}];
d=Map[(Count)[n,#]&,Union[n]];d=abbr[Flatten[{o d[[1]],Sort[Rest[d]]}]];AppendTo[d,c]];

dico[g_]:=Module[{gg,o=1,n={}},
If[g=={{1}},Return[{1.}]];gg=If[Length[g]==1,g[[1]],g,gf];
gf=Sign[Flatten[gg]];
If[abelianQ[gg],o=1.];If[gg===Abs[gg],Null,o=-o;n={negco[gg]}];If[MemberQ[gf,I]||MemberQ[gf,-I],o=I o];If[MemberQ[gf,𝕁]||MemberQ[gf,(𝕁^2)],o=𝕁 o];If[MemberQ[gf,𝕐]||MemberQ[gf,(𝕐^2)],o=𝕐 o];If[Length[gg]==32,n={subgrpPerm[gg,0,4,4]}];If[Length[gg]==64,n={Max[orderCount[gg]],nabco[gg]}];If[Length[gg]==54||Length[gg]==72,n={subgrpPerm[gg,0,3,3]}];If[MemberQ[{128,129},Length[gg]],n={Max[orderCount[gg]],nabco[gg]}];Switch[Length[gg],81,Flatten[{o, trico[gg]}],_,abbr[distribution[Table[gg[[i,i]],{i,Length[gg]}]],o,n]]];trico[g_]:=abbr[If[Length[g]>1,distribution[Table[g[[i,g[[i,i]]]],{i,Length[g]}]],distribution[Table[g[[1,i,g[[1,i,i]]]],{i,Length[g[[1]]]}]]] ]

nabco[g_]:=If[Length[g]==1,Length[g[[1]]]^2-Length[Position[g[[1]]-Transpose[g[[1]]],0]],Length[g]^2-Length[Position[g-Transpose[g],0]]];
negco[g_]:=Length[Position[g-Abs[g],a_/;a≠0]];

subgrpPerm[g_,a_:0]:=Module[{p=Flatten[{1,Last/@Sort[({RandomReal[],#1}&)/@Range[Length[g]-1]]+1}]},subgroups[reorder[g,p],a]];subgrpPerm[g_,a_,b_,c_]:=Module[{p=Flatten[{1,Last/@Sort[({RandomReal[],#1}&)/@Range[Length[g]-1]]+1}]},subgroups[reorder[g,p],a,b,c]];

subgroupTypes[sg_:sg]:=Module[{c,l=Length[sg],j,g=gLTop,m=Length[Last[sg]],n,count,types={}},count=Table[0,{i,m}];Do[count[[Length[sg[[j]] ] ]]++,{j,l}];n=1;Do[c=count[[i]];If[c>0,If[PrimeQ[i],n+=c;AppendTo[types,{c,StringJoin["C",ToString[i]]}],
Do[AppendTo[types,{id[g,sg[[n]]]}];n++,{z,count[[i]]}]]],
{i,2,m}];
types]
collect[sg_:%]:=Module[{l=Length[sg],c={},s,s1},Do[If[Length[s=sg[[i]]]>1,AppendTo[c,s],s1=Position[c,s[[1]]];If[s1=={},AppendTo[c,{1,s[[1]]}],s1=s1[[1,1]];c[[s1,1]]=c[[s1,1]]+1]],{i,l}];c]

10.12 Generalised Hoop Algebra Routines toPolar etc, hoopTimes, hoopInverse, hoopPower.

toPolar[{a__},g_:gName]:=toPol[{a},g];
tohyPolar[{a__},g_:gName]:=tohyPol[{a},g];
tohyVector[{a__},g_:gName]:=tohyVec[{a},g];

hoopTimes[a_?VectorQ,b_?VectorQ,g_?MatrixQ]:=Module[{ab,i,j,s,ss,u=Table[0,{k,mm=Length[g]}]},
ab=u;Rl=u;Rr=u;i=Join[a,u];j=Join[b,u];
Do[Do[s=g[[l,k]];ss=Sign[s];
ab[[s/ss]]+=i[[l]] j[[k]] ss,{k,mm}],{l,mm}];
ab];
hoopTimes[a_?VectorQ,b_?VectorQ,g_]/;Head[g]===String:=hoopTimes[gLoop=mp[g];gName=g;mm=Length[g];a,b]
hoopTimes[a_?VectorQ,b_?VectorQ]:=Module[{ab,i,j,p,s,ss,u},u=Table[0,{kk,mm(*=Length[gLoop]*)}];ab=u;
i=Join[a,u];j=Join[b,u];(*0 Pad to full length*)
Do[Do[s=gLoop[[l,k]];ss=Sign[s];(*Signed-table Vector multiplication*)
ab[[s/ss]]+=i[[l]] j[[k]] ss,{k,mm}],{l,mm}];
Rl=u;Rr=u;sd[gName];
(*Check remainders if shape[ab] is known & has zeroes*)If[sh≠{{{}}}&&(p=Position[Simplify[shape[ab]],0])≠{},
If[Complement[p,Position[shape[i],0]]≠{},(*Rl needed. Calculate AiAB*)u=hoopInverse[j];
Do[Do[s=gLoop[[l,k]];ss=Sign[s];
Rl[[s/ss]]+=u[[k]] ab[[l]] ss,{k,mm}],{l,mm}];Rl=Chop[a-Rl]];
If[Complement[p,Position[shape[j],0]]≠{},(*Rr needed. Calculate ABBi*)u=hoopInverse[i];
Do[Do[s=gLoop[[l,k]];ss=Sign[s];
Rr[[s/ss]]+=ab[[k]]u[[l]]  ss,{k,mm}],{l,mm}];Rr=Chop[b-Rr]]
];ab]

hoopInverse[v_?VectorQ]:=Module[{arrsz,abcsz,ls,inv=Table[0,{ii,mm}],s,temp,var,vec},
sd[gLoop];vec=Take[Flatten[Append[v,inv]],mm];ls=Length[sh];
arrsz=Simplify[Table[Det[sh[[i]]/.fromVtoA[el,vec]],{i,ls}]/.rofu]/.rofu;
abcsz=Simplify[Table[Det[sh[[i]]],{i,ls}]/.rofu]/.rofu;
Do[s=Sign[gi[[ii]]];var=el[[gi[[ii]]/s]];temp=0;Do[Which[Abs[Chop[arrsz[[jj]],hmin]]===0,Null,
True,temp+=s gi[[mm+jj]](∂_var)abcsz[[jj]]/abcsz[[jj]]],{jj,ls}];inv[[ii]]+=temp,{ii,mm}];
Chop[Simplify[inv/mm/.fromVtoA[el,vec]]/.rofu]];

hoopPower[A_,r_:1/2]:=Module[{a={},lg,l},If[r<0,hoopPower[hoopInverse[A],-r],l=toPolar[A];lg=Length[gp];Do[AppendTo[a,If[IntegerQ[gp[[ii]]],If[Head[l[[ii]]]===Complex,((l[[ii]])^r),((Abs[l[[ii]]])^r)Sign[l[[ii]]],((l[[ii]])^r)],rl[[ii]]]],{ii,lg}];Chop[toVec[a,gName]]]];

hoopRoot[A_?VectorQ] :=Module[{a={},l=toPolar[A]},(* gp shows whether radius or angle *)
Do[AppendTo[a,If[IntegerQ[gp[[i]]],((Abs[l[[i]]])^(1/2))Sign[l[[i]]],l[[i]]/2]],
{i,Length[gp]}];Chop[toVec[a]]]

10.13 Substitutions  fa,  fp, pow2, power2, linearFactor, s2, s3, s4, pr1, pr2 .

fp[g_,p_:power2]/;Head[g]===TraditionalForm:=fp[g[[1]],p];
fp[g_?indexTableQ,p_:pow2]:=Module[{pp=p,lg=Length[g],lp=Length[p]},pp=If[lp<lg,Flatten[Append[pp,Table[0,{i,lg-lp}]]],Take[pp,lg]];pa=Factor[Det[gmap[g,pp]]];If[Length[fp]>1&&fp[[1]]==-1,-pa,pa,pa]];fa[g_,]/;Head[g]===TraditionalForm:=fa[g[[1]]];
fa[g_?indexTableQ]:=If[Length[g]<13,Flatten[If[(pa=Factor[Det[gmap[g,el2]]])[[1]]==-1,-pa,pa,pa]],Print["Too Long for fa"];Abort[]];

pow2=Flatten[Prepend[Table[(2^i),{i,0,63}],{ø}]];
power2=Flatten[Prepend[Table[(2^i),{i,0,61}],{"ø",3,7}]];
fromVtoA[Null]:={};
fromVtoA[vec_?VectorQ,a_:el]:=Table[vec[[ii]]->a[[ii]],{ii,Length[vec]}]

(* Permutation Lists *)
s3={{2,1,3},{3,1,2}};s4={{2,1,3,4},{1,2,4,3},{1,4,2,3},{3,4,1,2},{2,3,4,1}};
s5={{2,1,3,4,5},{1,2,4,5,3},{2,3,4,1,5},{1,4,5,2,3},{3,4,5,1,2},{2,3,4,5,1},{3,4,1,2,5},{1,2,4,3,5}};

10.14 Matrix Group Data u2, u3, u4.

u2={{{-1,0},{0,-1}},{{1,0},{0,-1}},{{0,-I},{I,0}},{{0,1},{1,0}},{{0,𝕐},{(𝕐^2),0}},{{𝕜,0},{0,𝕜}},{{0,(𝕟^4)},{(𝕟^3),0}},{{𝕞,0},{0,𝕞}},{{0,𝕏},{(𝕏^3),0}},{{𝕐,0},{0,(𝕐^2)}},{{𝕁,0},{0,(𝕁^2)}},{{I,0},{0,I}},{{0,I},{I,0}},{{0,-1},{1,0}},{{0,(𝕐^2)},{-𝕐,0}},{{𝕏,0},{0,(𝕏^3)}},{{0,-(𝕠^3)},{(𝕠^5),0}},{{𝕡,0},{0,(𝕡^4)}},{{𝕙,0},{0,(𝕙^5)}},{{(𝕐^2),0},{0,-𝕐}},{{𝕧,0},{0,(𝕧^6)}},{{𝕠,0},{0,(𝕠^7)}},{{𝕟,0},{0,(𝕟^8)}},{{0,1},{-1,0}},{{0,𝕐},{-𝕐^2,0}},{{0,𝕜},{-𝕜,0}},{{0,𝕞},{-𝕞,0}},{{0,𝕞},{-𝕞,0}}, {{0,1},{I,0}},{{1,0},{0,𝕤}},{{0,1},{𝕤,0}},{{0,1},{𝕐,0}},{{𝕐,0},{0,1}},{{I,0},{0,-I}},{{0,1},{𝕏,0}},{{(𝕐^2),0},{0,𝕐}}};

u3={{{-1,0,0},{0,-1,0},{0,0,-1}},{{1,0,0},{0,0,1},{0,1,0}},{{1,0,0},{0,𝕜,0},{0,0,𝕜}},{{-1,0,0},{0,-𝕜,0},{0,0,-𝕜}},{{0,1,0},{1,0,0},{0,0,1}},{{0,-1,0},{-1,0,0},{0,0,-1}},{{0,𝕐,0},{(𝕐^2),0,0},{0,0,1}},{{1,0,0},{0,𝕐,0},{0,0,(𝕐^2)}},{{0,0,𝕐},{𝕐,0,0},{0,𝕐,0}},{{0,0,1},{1,0,0},{0,1,0}},{{0,0,I},{I,0,0},{0,-1,0}},{{𝕐,0,0},{0,𝕐,0},{0,0,𝕐}},{{0,0,1},{0,1,0},{-1,0,0}},{{0,0,I},{0,1,0},{I,0,0}},{{1,0,0},{0,I,0},{0,0,-I}},{{1,0,0},{0,(𝕡^2),0},{0,0,(𝕡^3)}},{{-𝕐,0,0},{0,-𝕐,0},{0,0,-𝕐}},{{-1,0,0},{0,-𝕐,0},{0,0,-(𝕐^2)}},{{(𝕐^2),0,0},{0,0,(𝕐^2)},{0,(𝕐^2),0}},{{0,0,-I},{-I,0,0},{0,1,0}},{{0,1,0},{0,0,1},{-1,0,0}},{{𝕐,0,0},{0,-𝕐,0},{0,0,-𝕐}},{{0,0,-𝕐},{-𝕐,0,0},{0,-𝕐,0}},{{1,0,0},{0,(𝕧^2),0},{0,0,(𝕧^5)}},{{0,1,0},{I,0,0},{0,0,I}},{{I,0,0},{0,0,1},{0,I,0}},{{𝕠,0,0},{0,1,0},{0,0,(𝕠^7)}},{{1,0,0},{0,(𝕟^4),0},{0,0,(𝕟^5)}},{{-1,0,0},{0,-(𝕡^2),0},{0,0,-(𝕡^3)}},{{-1,0,0},{0,-(𝕧^2),0},{0,0,-(𝕧^5)}},{{-1,0,0},{0,-(𝕟^4),0},{0,0,-(𝕟^5)}},{{1,0,0},{0,𝕁,0},{0,0,(𝕁^2)}},{{𝕟,0,0},{0,𝕟,0},{0,0,(𝕟^7)}},{{0,-1,0},{1,0,0},{0,0,1}},{{0,-1,0},{0,0,-1},{1,0,0}},{{1,0,0},{0,0,-1},{0,1,0}},{{0,𝕡,0},{(𝕡^3),0,0},{0,0,(𝕡^2)}},{{-1,0,0},{0,1,0},{0,0,-1}},{{0,0,-1},{0,1,0},{1,0,0}},{{1,0,0},{0,-1,0},{0,0,1}},{{0,0,1},{0,-1,0},{-1,0,0}},{{0,0,-1},{0,-1,0},{1,0,0}},{{I,0,0},{0,I,0},{0,0,I}},{{-I,0,0},{0,-I,0},{0,0,-I}},{{0,1,0},{0,0,I},{1,0,0}},{{0,I,0},{0,0,I},{I,0,0}},{{0,𝕤,0},{0,0,1},{1,0,0}}};

u4={{{1,0,0,0},{0,1,0,0},{0,0,-1,0},{0,0,0,-1}},{{0,1,0,0},{1,0,0,0},{0,0,-1,0},{0,0,0,-1}},{{1,0,0,0},{0,0,-1,0},{0,-1,0,0},{0,0,0,1}},{{0,1,0,0},{1,0,0,0},{0,0,0,1},{0,0,1,0}},{{-1,0,0,0},{0,1,0,0},{0,0,-1,0},{0,0,0,1}},{{1,0,0,0},{0,-1,0,0},{0,0,-1,0},{0,0,0,1}},{{0,0,1,0},{0,0,0,-1},{1,0,0,0},{0,-1,0,0}},{{1,0,0,0},{0,1,0,0},{0,0,𝕐,0},{0,0,0,(𝕐^2)}},{{0,0,-1,0},{1,0,0,0},{0,-1,0,0},{0,0,0,1}},{{1,0,0,0},{0,0,0,𝕐},{0,𝕐,0,0},{0,0,𝕐,0}},{{1,0,0,0},{0,𝕐,0,0},{0,0,𝕐,0},{0,0,0,𝕐}},{{1,0,0,0},{0,-1,0,0},{0,0,I,0},{0,0,0,I}},{{0,0,-1,0},{0,0,0,-1},{0,1,0,0},{1,0,0,0}},{{0,0,0,-1},{0,0,1,0},{0,-1,0,0},{1,0,0,0}},{{0,0,-1,0},{0,0,0,1},{1,0,0,0},{0,-1,0,0}},{{0,-1,0,0},{1,0,0,0},{0,0,0,-1},{0,0,1,0}},{{1,0,0,0},{0,𝕡,0,0},{0,0,(𝕡^2),0},{0,0,0,(𝕡^2)}},{{0,1,0,0},{0,0,-1,0},{-1,0,0,0},{0,0,0,-1}},{{1,0,0,0},{0,𝕙,0,0},{0,0,(𝕙^2),0},{0,0,0,(𝕙^3)}},{{𝕧,0,0,0},{0,𝕧,0,0},{0,0,(𝕧^2),0},{0,0,0,(𝕧^3)}},{{1,0,0,0},{0,0,-I,0},{0,-1,0,0},{0,0,0,I}},{{1,0,0,0},{0,1,0,0},{0,0,(𝕠^3),0},{0,0,0,(𝕠^5)}},{{1,0,0,0},{0,𝕟,0,0},{0,0,(𝕟^4),0},{0,0,0,(𝕟^4)}},{{1,0,0,0},{0,0,-(𝕡^2),0},{0,-𝕡,0,0},{0,0,0,(𝕡^2)}},{{-1,0,0,0},{0,-𝕡,0,0},{0,0,-(𝕡^2),0},{0,0,0,-(𝕡^2)}},{{0,0,-I,0},{1,0,0,0},{0,-1,0,0},{0,0,0,I}},{{0,0,𝕐,0},{0,0,0,(𝕐^2)},{-1,0,0,0},{0,-1,0,0}},{{0,0,-(𝕡^2),0},{1,0,0,0},{0,-𝕡,0,0},{0,0,0,(𝕡^2)}},{{0,0,0,1},{0,0,1,0},{0,-1,0,0},{-1,0,0,0}},{{0,0,0,-I},{0,0,I,0},{0,I,0,0},{-I,0,0,0}},{{0,0,1,0},{0,0,0,-1},{-1,0,0,0},{0,1,0,0}},{{0,0,0,1},{0,0,1,0},{0,1,0,0},{1,0,0,0}},{{0,𝕐,0,0},{𝕐,0,0,0},{0,0,0,1},{0,0,𝕐,0}},{{0,0,𝕐,0},{0,0,0,(𝕐^2)},{(𝕐^2),0,0,0},{0,𝕐,0,0}},{{0,1,0,0},{1,0,0,0},{0,0,0,-1},{0,0,-1,0}},{{0,1,0,0},{0,0,0,-1},{-1,0,0,0},{0,0,1,0}},{{0,1,0,0},{0,0,1,0},{0,0,0,1},{-1,0,0,0}},{{0,-I,0,0},{I,0,0,0},{0,0,0,-I},{0,0,I,0}},{{0,0,-I,0},{0,0,0,-I},{I,0,0,0},{0,I,0,0}},{{0,0,1,0},{0,0,0,1},{1,0,0,0},{0,1,0,0}},{{0,0,-1,0},{0,0,0,-1},{1,0,0,0},{0,1,0,0}},{{0,0,0,1},{0,0,-1,0},{0,-1,0,0},{1,0,0,0}},{{0,1,0,0},{-1,0,0,0},{0,0,0,1},{0,0,-1,0}},{{0,0,0,-1},{0,0,-1,0},{0,1,0,0},{1,0,0,0}},{{0,I,0,0},{-I,0,0,0},{0,0,0,-I},{0,0,I,0}},{{0,1,0,0},{-1,0,0,0},{0,0,0,-1},{0,0,1,0}},{{0,-I,0,0},{-I,0,0,0},{0,0,0,I},{0,0,I,0}},{{-I,0,0,0},{0,I,0,0},{0,0,I,0},{0,0,0,-I}},{{0,I,0,0},{I,0,0,0},{0,0,0,-I},{0,0,-I,0}},{{0,0,-1,0},{0,0,0,-1},{-1,0,0,0},{0,-1,0,0}},{{0,𝕤,0,0},{0,0,0,1},{1,0,0,0},{0,0,1,0}}};

10.15 Clifford (Geometric) Algebras CLpq ,cij, ijc, lp, cLoop, cTimes, cT, cInverse, cRef, cRot, cShape etc.

(* Creates gLoop if p+q<5 or r≠0. -6<r<6 extends to include Oct and Ternal*)
cLoop[p0_,q_:0,r_:0]:=Module[{a,b,j,k,p=IntegerPart[p0],tmp},gLoop={};cDimensions=p+q;lp=(2^p);mm=2^cDimensions;cSparse=False;
Switch[Abs[r],
1,gLoop=cd[{-1,-1,-1}];lp=0;mm=8;el=Take[el2,8];gName="Octr",
2,gLoop=cd[{1,-1,-1}];lp=2;mm=8;el=Take[el2,8];gName="Octi",
3,gLoop={{1,2,3},{2,3,1},{3,1,2}};lp=2;mm=3;el={ø,𝕒,𝕒2};gName="C3",
4,gLoop=cd[{1,1,-1.}];lp=2;mm=8;el=Take[el2,8];gName="O4",
_,lp=(2^p);cSparse=If[p+q<5||!IntegerQ[p0],False,True];
If[!cSparse,gLoop=Table[
Which[i==1,j,j==1,i,True,cij[i,j]]
,{i,mm},{j,mm}]
];el=Take[el2,mm];gName="CL"<>ToString[p]<>ToString[q]
];(*End Switch*)
If[r<0,(*Triple the table*)
a=Sign[gLoop];b=Abs[gLoop];tmp=Table[Table[a (b +mm Mod[i+j-2,3]),{i,3}],{j,3}];gLoop={};
Do[j=Plus[Floor[Times[Plus[h,-1],Power[mm,-1]]],1];k=Mod[h,mm,1];
AppendTo[gLoop,
Flatten[Table[tmp[[i,j]][[k]],{i,3}]]
],{h,3 mm}];
gName=gName<>"C3";cDimensions+=2;mm*=3;el=Take[el3,mm]];
gLoop];

cGrading:=Module[{a},a=Table[{},{cDimensions+1}];a[[1]]={1};
Do[AppendTo[a[[Plus@@IntegerDigits[i-1,2]+1]],i],{i,2,mm}];a];
cGrInv={{1,2},{1,2,3,4},{1,2,3,5,4,6,7,8},{1,2,3,6,4,7,8,12,5,9,10,13,11,14,15,16},{1,2,3,7,4,8,9,17,5,10,11,18,12,19,20,27,6,13,14,21,15,22,23,28,16,24,25,29,26,30,31,32},{1,2,3,8,4,9,10,23,5,11,12,24,13,25,26,43,6,14,15,27,16,28,29,44,17,30,31,45,32,46,47,58,7,18,19,33,20,34,35,48,21,36,37,49,38,50,51,59,22,39,40,52,41,53,54,60,42,55,56,61,57,62,63,64},{1,2,3,9,4,10,11,30,5,12,13,31,14,32,33,65,6,15,16,34,17,35,36,66,18,37,38,67,39,68,69,100,7,19,20,40,21,41,42,70,22,43,44,71,45,72,73,101,23,46,47,74,48,75,76,102,49,77,78,103,79,104,105,121,8,24,25,50,26,51,52,80,27,53,54,81,55,82,83,106,28,56,57,84,58,85,86,107,59,87,88,108,89,109,110,122,29,60,61,90,62,91,92,111,63,93,94,112,95,113,114,123,64,96,97,115,98,116,117,124,99,118,119,125,120,126,127,128}};

cFullBasis[e_String:""]:=Module[{g0,m,res={},temp},m=If[Divisible[mm,3],mm/3,mm];g0=Table[IntegerDigits[i,2],{i,0,m-1}];Do[temp=e;Do[temp=temp<>ToString[g0[[i,j]]],{j,Length[g0[[i]]]}];AppendTo[res,temp],{i,Length[g0]}];
If[mm≠m,AppendTo[res,{"𝕁" res}]];
Flatten[res]]

(*Compiled product of Clifford elements. lp is no. of p monovectors.*)
cij=Compile[{{i,_Integer},{j,_Integer}},Module[{a,b={},bb={},c={0},d,mx=Max[i,j]},a=Reverse[IntegerDigits[i-1,2]];Do[If[a[[k]]≠0,AppendTo[b, 2 k]],{k,Length[a]}];bb=b;a=Reverse[IntegerDigits[j-1,2]];
Do[If[a[[k]]≠0,AppendTo[b, 2 k+1];If[(2^k)>lp,AppendTo[c, 2 k]]],{k,Length[a]}];d=If[mx>lp&&OddQ[Length[Intersection[bb,c]]],-1,1]*(BitXor[i-1,j-1]+1)*Signature[b]]];

ijc[i_,j_]:=BitXor[i-1,j-1]+1;

cLL[AS_]:=Module[{A=ArrayRules[cT[AS,AS]]},If[A[[1,1]]=={1},A[[1,2]],0]]/;Head[AS]==SparseArray

cTimes[aa_,bb_,o_:0]:=Module[(*First unpack, pad, & sparsify vectors*){as=ArrayRules[SparseArray[tocFlat[aa]]],ai,av,la,bs=ArrayRules[SparseArray[tocFlat[bb]]],bi,bv,lb,
G,L,i,j,s,t,va},If[!Take[Characters[gName],2]==={"C","L"},Print["Not A Clifford Algebra"];Abort[]];
la=Min[Length[as]-1,mm];ai=Table[as[[i,1,1]],{i,la}];av=Table[as[[i,2]],{i,la}];
lb=Min[Length[bs]-1,mm];bi=Table[bs[[i,1,1]],{i,lb}];bv=Table[bs[[i,2]],{i,lb}];
(*set up global lists for Geom and Lie products*)
G=Table[0,{mm}];L=G;Cl=.;Jo=.;Li=.;
(*Sum Geom and Lie product signed element products*)
Do[i=ai[[ii]];va=av[[ii]];
Do[j=bi[[jj]];s=cij[i,j];
G[[Abs[s]]]+=Sign[s] va bv[[jj]];
If[o>0,s=cij[j,i];(*L index*)
L[[Abs[s]]]+=Sign[s]va bv[[jj]]],
{jj,lb}],
{ii,la}];
Cl=Chop[Simplify[If[cSparse,SparseArray[G],G]]];If[o==1,cBA=Chop[Simplify[L]];If[cSparse,cBA=SparseArray[cBA]]];
If[o>1,Li=Chop[Simplify[(G-L)/2]];Jo=Chop[Simplify[(G+L)/2]];If[cSparse,Li=SparseArray[Li];Jo=SparseArray[Li]]];
Switch[o,
0,Cl,
1,Cl(* sets cBA *),
-1,-cTimes[Cl,aa],(*reflection*)
2,Jo,
3,Li,
4,{Jo,Li},
5,{Cl,Li,Jo},
6,cTimes[Cl,cInverse[aa]],
_,{Cl,Li,Jo}]];

cT[aa_,bb_]:=(*Minimal multiplication of SparseArrays*)Module[{a=ArrayRules[aa],ai,av,b=ArrayRules[bb],bi,bv,G=Table[0,{mm}],i,ij,la,lb,v},la=Length[a]-1;ai=Table[a[[i,1,1]],{i,la}];av=Table[a[[i,2]],{i,la}];
lb=Length[b]-1;bi=Table[b[[i,1,1]],{i,lb}];bv=Table[b[[i,2]],{i,lb}];
Do[i=ai[[ii]];v=av[[ii]];
Do[ij=cij[i,bi[[jj]]];
G[[Abs[ij]]]+=Sign[ij] v bv[[jj]],
{jj,lb}],
{ii,la}];
SparseArray[Chop[Simplify[G]]]]/;(Head[aa]==SparseArray&&Head[bb]==SparseArray)

cT1[aa_,bb_]:=(*Minimal Clifford multiplication of
SparseArrays, creating Cl & cBAS*)Module[{a=ArrayRules[aa],ai,av,b=ArrayRules[bb],bi,bv,G=Table[0,{mm}],i,ij,j,L,la,lb,v,va},L=G;la=Length[a]-1;ai=Table[a[[i,1,1]],{i,la}];av=Table[a[[i,2]],{i,la}];
lb=Length[b]-1;bi=Table[b[[i,1,1]],{i,lb}];bv=Table[b[[i,2]],{i,lb}];
Do[i=ai[[ii]];va=av[[ii]];
Do[j=bi[[jj]];vb=bv[[jj]];ij=cij[i,j];
G[[Abs[ij]]]+=Sign[ij] va vb;
ij=cij[j,i];(*L index*)
L[[Abs[ij]]]+=Sign[ij]va vb,
{jj,lb}],
{ii,la}];
cBAS=SparseArray[-Chop[Simplify[L]]];
Li=SparseArray[Chop[Simplify[(G-L)/2]]];
Cl=SparseArray[Chop[Simplify[G]]]]/;(Head[aa]==SparseArray
&&Head[bb]==SparseArray)

cRef[un_,A0_]:=(* unit vector reflecting a list of multivectors, no tests*)Table[cT[cT[SparseArray[un],SparseArray[A0[[i]]]],SparseArray[-un]],{i,Length[A0]}];

cRefS[unS_,A0S_]:=(* unit SparseArray reflecting a list of SparseArrays, no tests*)Table[cT[cT[unS,A0S[[i]]],-unS],{i,Length[A0S]}];

cRotate[m_,n_,M_]:=Module[{mS=SparseArray[m],nS=SparseArray[n],MS=SparseArray[M]},cT[cT[cT1[mS,nS],MS],cBAS]/Abs[cLL[mS]cLL[nS]]];

cRot[mS_,nS_,AS_]:=(* unit SparseArrays rotating an array of SparseArrays, no tests*)Module[{mn=cT1[mS,nS]},Table[cT[cT[mn,AS[[i]]],cBAS],{i,Length[AS]}]];

cShape[a_?VectorQ,g_:gName]:=Chop[Table[Det[sh[[i]]/.fromVtoA[el,a]]/.rofu,{i,Length[sh]}],hmin];
cShape[a_,g_:gName]:=Chop[sh/.fromVtoA[el,tocFlat[a]],hmin];

tocGr[Ao_,gr_:0]:=Module[{A=tocFlat[Ao]},cGrading/.Table[If[MemberQ[If[gr >0,cGrading[[gr+1]],Flatten[cGrading]],i],i->A[[i]],i->0 ],{i,mm}]];

cGr[M_,n_:0]:=If[VectorQ[M],tocGr[M][[n+1]],M[[n+1]]];

tocSparse[V_?MatrixQ]:=V;
tocSparse[V_?VectorQ]:=SparseArray[V];
tocSparse[V_]:=SparseArray[tocFlat[V]];

tocFlat[grv_]:=Which[
MatrixQ[grv],tgr=Table[0,{i,mm}];(*Inserts non-zeroes*)Do[If[grv[[i,1]]≤mm,tgr[[grv[[i,1]]]]=grv[[i,2]]],{i,Length[grv]}];tgr,

VectorQ[grv],tgr=grv;(*Simply Right-pads with zeroes*)tgr=Take[Flatten[AppendTo[tgr,Table[0,{i,mm}]]],mm],

True,(*Flatten a graded list*)Table[Flatten[grv][[cGrInv[[cDimensions,i]]]],{i,Min[Length[Flatten[grv]],mm]}]
];

cInverse[v0_]:=Module[{arrsz,abcsz,inv=Table[0,{i,mm}],ls,s,saEl,v=SparseArray[tocFlat[v0]],v1,var,vec,temp},If[!Take[Characters[gName],2]==={"C","L"},Print["Not A Clifford Algebra"];Abort[]];
sd[gName];ls=Length[sh];v1=Most[ArrayRules[v]];saEl=SparseArray[Table[Rule[v1[[i,1]],el[[v1[[i,1,1]]]]],{i,Length[v1]}],{mm}];abcsz=shape[saEl];
arrsz=Expand[Table[Det[sh[[i]]/.fromVtoA[el,v]],{i,ls}]/.rofu];
abcsz=Table[Det[sh[[i]]],{i,ls}];ls=Length[arrsz];
Do[s=Sign[gi[[ii]]];var=el[[gi[[ii]] s]];temp=0;Do[Which[Abs[Chop[arrsz[[jj]],hmin]]===0,Null,
True,temp+=s gi[[mm+jj]](∂_var)abcsz[[jj]]/abcsz[[jj]]],
{jj,ls}];inv[[ii]]+=temp,
{ii,mm}];
Chop[Simplify[inv/mm/.fromVtoA[el,v]/.rofu]]];

10.16 Gap Data Access, dsRuleExpand, fromdb, fromSizeList, gapInverse, gapShape, gapTimes, pgcd, prs, toDs.

dsRuleExpand[a___]:=(*ba->c becomes 𝕓𝕒->𝕔 etc*)Table[Rule[stringExpand[toDs[ToString[a[[i,1]]]]],stringExpand[toDs[ToString[a[[i,2]]]]]],{i,Length[a]}];

fromdb[m_,n_,o_:0,f_:{}]:=Module[{f1},{ack,irrepReal,gapName,gapel,gapGens,gapRels,irrep,gapCycles}=Read[fromdbZ[m,n],{Expression,Expression,String,Expression,Expression,Expression,Expression,Expression}];
im=Length[irrep];jm=Length[irrep[[1]]];gapPerm=.;irreplen=Table[Length[irrep[[i,1]]],{i,im}];If[gapGens≠{},(*PC*)gapRels=dsRuleExpand[gapRels]];
gapel=toDs[gapel];gLinv=.;gapLoop=.;mm=m;𝕣=m;
If[o>0,gapLoop=ge[gapGens,gapRels,0,f];sd[gapName]];
If[o<0,f1=Intersection[gapGens,f];gapCycles=Drop[gapCycles,f1-1];gapLoop=GroupMultiplicationTable[gapPerm=PermutationGroup[Map[Cycles,gapCycles,{1}]]]];
gLinv=gInverse[gapLoop];
Close[tempin]];

fromdbZ[m_,n_,d_:"C:\\Program Files\\Wolfram Research\\Mathematica\\8.0\\AddOns\\ExtraPackages\\rhb\\sg"]:=tempin=OpenRead[d<>ToString[m]<>"_"<>ToString[n]<>".txt"];

fromSizeList[SL_:sizeList]:=Module[{gLin=gInverse[gapLoop]},If[im≠mm,Return["Non-Abelian"]];prs[Plus@@(SL*Table[Det[irrep[[i,gLin[[j]]]]]*irreplen[[i]]^2,{i,im},{j,jm}])]/jm]

gapInv[i_,j_]:=irrep[[i,gLinv[[j]]]];
gapInv[M_]:=prs[dM=Det[M];dM*Inverse[M]pgcd[dM]];
gapInverse[A_]:=Module[{vs=Table[Plus@@(A*irrep[[i]]),{i,im}]},
prs[Table[Plus@@Table[(If[vs[[i]]==={{0}},0,
	Tr[gapInv[irrep[[i,j]].vs[[i]]]]/.Tr[0]->0]*irreplen[[i]]),{i,im}]/jm,{j,jm}]]];

gapShape[V0_?VectorQ]:=Module[{i,j,im=Length[irrep],jm=Length[irrep[[1]]],k,res={},st,Vo},Vo=Take[Join[V0,Table[0,{j,jm}]],jm];(*Pad,chop*)st=Table[prs[Det[Plus@@Table[Vo [[j]]irrep[[i,j]],{j,jm}]]],
{i,im}];
sizeList=st(*global table of sizes, some involving s.*);
i=0;While[i++;i<=Length[irrepReal],(*Sum sublists for reals*)
j=0;k=1;While[j++;j<=Length[irrepReal[[i]]],
k*=st[[irrepReal[[i,j]]]]
](*End While j*);AppendTo[res,prs[k]];
](*End While i*);
Chop[res/.Solve[s^𝕣==1.][[2]]]];

gapTimes[vA_,vB_,g_:gapLoop]:=Module[{ab,m=Length[g],s,ss},If[Length[vA]==m&&Length[vB]==m,ab=Table[0,{i,m}];
Do[
Do[s=g[[l,k]];ss=Sign[s];
ab[[s ss]]+=vA[[k]] vB[[l]] ss,
{k,mm}],
{l,mm}],
ab="Length Error"];
ab]

pgcd[p_]:=Expand[PolynomialExtendedGCD[p,Cyclotomic[𝕣,s],s][[2,1]]];Attributes[pgcd]={Listable,Protected};

prs[p_]:=PolynomialRemainder[Expand[p],Cyclotomic[𝕣,s],s];Attributes[prs]={Listable,Protected};

toDs[str_]:=(*o,a..g becomes ø,𝕒...𝕘*)Module[{chc=If[StringQ[str],ToCharacterCode[str],ToCharacterCode[ToString[str]]]},stringExpand[ToExpression[FromCharacterCode[chc/.{97->63206,98->63207,99->63208,100->63209,101->63210,102->63211,103->63212,111->248}]]]]

11. End private context. Unprotect some exported symbols, end package context.

End[];

Protect[Evaluate[$Context <> "*"]];

Unprotect[{a,A,a1,a2,a3,a4,aa,ab,AB,abc,abcd,abcde,abcdef,abcdf,abce,abcef,abcf,abd,abde,abdef,abdf,abe,abef,abf,ac,acd,acde,acdef,acdf,ace,acef,acf,ad,ade,adef,adf,ae,aef,af,agek,ai,Ai,AiAB,AiBA,Am,any,ap,Ap,ar,as,ayz,azx,b,B,b1,b2,b3,b4,BA,bb,bc,bcd,bcde,bcdef,bcdf,bce,bcef,bcf,bd,bde,bdef,bdf,be,bef,bf,c,c1,c2,c3,c4,cBA,cBAS,cd,cde,cdef,cdf,cDimensions,ce,cef,cf,cGr,cGrading,Cl,cr,cSparse,c𝕀,c1Toc2,c2Toc1,d,d1,da,dab,db,de,def,df,e,e1,el2,ef,el,f,f2,fa,ff,fi,fj,fn,fp,g,G,g1,g2,gapCycles,gapel,gapGens,gapLoop,gapName,gapPerm,gapRels,gel,genel,gens,gf,gg,gi,gLinv,gLoop,gLTop,gName,gp,h,h1,hh,i,i1,i2,ii,im,in,j,jj,jm,Jo,k,kk,l,la,Li,lm,lp,lr,ls,lt,m,m1,matel,mi,mm,n,nb,nn,no,np,nw,nx,ø,o1,o2,o3,o4,ok,oo,p,p1,p2,p22,p23,p26,pa,pab,papb,pb,pba,permel,pi,plex,po,pp,pr,ps,q,q22,q23,q24,q26,qq,r,r3,r4,r5,r6,r7,r8,r9,R1,R2,r22,r23,r26,rels,res,result,rhs,Rl,rofu,rr,Rr,rofu,rU,s,s22,s23,s24,s26,sab,sd,sg,sh,si,sij,sizeList,sm,irrep,smatI,smax,irreplen,irrepReal,ss,strep,t,temp,tempin,tes,test,tf,ts,u,uu,v,var,vec,vf,vv,w,x,x2,x4,xy,y,y2,z,𝕙,𝕜,𝕞,𝕟,𝕠,𝕡,𝕣,𝕤,𝕧,𝕏,𝕐}];

EndPackage[];