Symmetry Operations of Crystallographic Point Groups and Space Groups

Xianlong Wang, Ph.D.
      
      Max-Planck-Institut für Chemische Physik fester Stoffe 
      Nöthnitzer Str.40 
      D-01187 Dresden, Germany 
      Phone:49-351-4646-4424 
      Email:chem.wang@gmail.com

Introduction

There are 32 crystallographic point groups and 230 space groups in the three-dimensional space. Symmetry operations of them are given in the vector form in this notebook. For the space groups, both the operations for general positions and for the unique generators are included. A function to convert the vector form to the affine matrix form is given; the affine matrix consists of the transformation matrix and the shift vector. An additional function is written to give the transformation matrix only if the shift is unnecessary, i.e. the shift vector={0,0,0}. In chemistry and physics, it is interesting sometimes to know whether a point group is contained in some space groups. A short script has been written to generate the correspondence table between the two.
The notebook is useful for those who work on crystal structure manipulation.

Crystallographic Point Group

Symmetry  operations for crystallographic point groups (32 in total). The first element of the list for each point group is the label for the group in two forms: Schonflies notation and Hermann-Mauguin notation.
Source: Bilbao Crystallographic Server bcs Point Group Tables.
See: M.I.Aroyo, A.Kirov,C.Capillas, J.M.Perez-Mato & H.Wondratschek. "Bilbao Crystallographic Server II: Representations of crystallographic point groups and space groups".Acta Cryst.(2006),A62,115-128. 
Aroyo et al. "Bilbao Crystallographic Server: Databases and crystallographic computing programs".Zeitschrift fuer Kristallographie,(2006),221,1,015-027. 
http://www.cryst.ehu.es/index.html#retrieval.  Access Date:July 05,2006.

\(\(\(PointGroupOperations = {{"C1(1)", {x, y, 
              z}}, {"Ci(-1)", {x, y, 
              z}, {\(-x\), \(-y\), \(-z\)}}, {"C2(2)", {x, y, 
              z}, {\(-x\), y, \(-z\)}}, {"Cs(m)", {x, y, z}, {x, \(-y\), 
              z}}, {"C2h(2/m)", {x, y, z}, {\(-x\), 
              y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\), 
              z}}, {"D2(222)", {x, y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}}, {"C2v(mm2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x, \(-y\), z}, {\(-x\), y, 
              z}}, {"D2h(mmm)", {x, y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, z}}, {"C4(4)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}}, {"S4(-4)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}}, {"C4h(4/m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}}, {"D4(422)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}}, {"C4v(4mm)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {x, \(-y\), z}, {\(-x\), y, z}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"D2d(-42m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"D4h(4/mmm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"C3(3)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}}, {"C3i(-3)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - y, 
              x, \(-z\)}}, {"D3(32)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}}, {"C3v(3m)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-y\), \(-x\), z}, {\(-x\) + y, 
              y, z}, {x, x - y, z}}, {"D3d(-3m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"C6(6)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}}, {"C3h(-6)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {x, 
              y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + 
                y, \(-x\), \(-z\)}}, {"C6h(6/m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, 
              z}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - y, 
              x, \(-z\)}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + 
                y, \(-x\), \(-z\)}}, {"D6(622)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, 
              y, \(-z\)}, {x, x - y, \(-z\)}}, {"C6v(6mm)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, z}, {x - y, x, 
              z}, {\(-y\), \(-x\), z}, {\(-x\) + y, y, z}, {x, x - y, z}, {y, 
              x, z}, {x - y, \(-y\), z}, {\(-x\), \(-x\) + y, 
              z}}, {"D3h(-6m2)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"D6h(6/mmm)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, z}, {x - y, x, z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, 
              y, \(-z\)}, {x, 
              x - y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}, {y, x, 
              z}, {x - y, \(-y\), z}, {\(-x\), \(-x\) + y, 
              z}}, {"T(23)", {x, y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}}, {"Th(m-3)", {x, y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}}, {"O(432)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), \(-z\)}, {\(-x\), y, \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), x, \(-y\)}, {\(-z\), \(-x\), 
              y}, {y, z, x}, {\(-y\), z, \(-x\)}, {\(-y\), \(-z\), 
              x}, {y, \(-z\), \(-x\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-y\), x, 
              z}, {y, \(-x\), z}, {x, z, \(-y\)}, {\(-x\), z, y}, {x, \(-z\), 
              y}, {\(-x\), \(-z\), \(-y\)}, {z, y, \(-x\)}, {z, \(-y\), 
              x}, {\(-z\), \(-y\), \(-x\)}, {\(-z\), y, 
              x}}, {"Td(-43m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), \(-z\)}, {\(-x\), y, \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), x, \(-y\)}, {\(-z\), \(-x\), 
              y}, {y, z, x}, {\(-y\), z, \(-x\)}, {\(-y\), \(-z\), 
              x}, {y, \(-z\), \(-x\)}, {y, x, z}, {\(-y\), \(-x\), 
              z}, {\(-y\), x, \(-z\)}, {y, \(-x\), \(-z\)}, {x, z, 
              y}, {\(-x\), z, \(-y\)}, {x, \(-z\), \(-y\)}, {\(-x\), \(-z\), 
              y}, {z, y, x}, {z, \(-y\), \(-x\)}, {\(-z\), \(-y\), 
              x}, {\(-z\), y, \(-x\)}}, {"Oh(m-3m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x, \(-y\), \(-z\)}, {\(-x\), 
              y, \(-z\)}, {z, x, y}, {z, \(-x\), \(-y\)}, {\(-z\), 
              x, \(-y\)}, {\(-z\), \(-x\), y}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {\(-y\), \(-z\), x}, {y, \(-z\), \(-x\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-y\), x, 
              z}, {y, \(-x\), z}, {x, z, \(-y\)}, {\(-x\), z, y}, {x, \(-z\), 
              y}, {\(-x\), \(-z\), \(-y\)}, {z, y, \(-x\)}, {z, \(-y\), 
              x}, {\(-z\), \(-y\), \(-x\)}, {\(-z\), y, 
              x}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {\(-x\), y, 
              z}, {x, \(-y\), z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, \(-x\), y}, {z, 
              x, \(-y\)}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {y, 
              z, \(-x\)}, {\(-y\), z, x}, {\(-y\), \(-x\), z}, {y, x, 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {\(-x\), \(-z\), 
              y}, {x, \(-z\), \(-y\)}, {\(-x\), z, \(-y\)}, {x, z, 
              y}, {\(-z\), \(-y\), x}, {\(-z\), y, \(-x\)}, {z, y, 
              x}, {z, \(-y\), \(-x\)}}};\)\(
\)
    \)\)

Crystallographic Space Group

Symmetry operations for crystallographic space groups (230 in total). The first element of the list for each space group in SpaceGroupGenerators corresponds to the space group number. For the table of SpaceGroupOperations, the space group number along with the Hermann-Mauguin notation is given as the first element for the list of the group. For the space groups with two possible choices of crystal axes, only the 2nd choice given in Bilbao Crystallographic Server [see the references below] is included here. For example, for the space groups 146, 148, 160, 161, 166 and 167, the hexagonal axes are used for the tables.

Space Group Generators

(*Unique generators are given here . 
          Symmetry operations for all general points are given after this.*) 
 (*The first element of the list for each group is the space group number for the group*) 
SpaceGroupGenerators = {{1, {x, y, z}}, {2, {x, 
              y, z}, {-x, -y, -z}}, {3, {x, y, z}, {-x, 
              y, -z}}, {4, {x, y, z}, {-x, y + 1/2, -z}}, {5, {x, 
              y, z}, {-x, y, -z}, {x + 1/2, y + 1/2, z}}, {6, {x, y, 
              z}, {x, -y, z}}, {7, {x, y, z}, {x, -y, 
              z + 1/2}}, {8, {x, y, z}, {x, -y, z}, {x + 1/2, y + 1/2, 
              z}}, {9, {x, y, z}, {x, -y, z + 1/2}, {x + 1/2, y + 1/2, 
              z}}, {10, {x, y, z}, {-x, 
              y, -z}, {-x, -y, -z}}, {11, {x, y, z}, {-x, 
              y + 1/2, -z}, {-x, -y, -z}}, {12, {x, y, 
              z}, {-x, y, -z}, {-x, -y, -z}, {x + 1/2, 
              y + 1/2, z}}, {13, {x, y, z}, {-x, 
              y, -z + 1/2}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}}, {14, {x, y, 
              z}, {-x, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {15, {x, y, 
              z}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
              z}}, {16, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}}, {17, {x, y, z}, {-x, -y, 
              z + 1/2}, {-x, y, -z + 1/2}}, {18, {x, y, 
              z}, {-x, -y, z}, {-x + 1/2, 
              y + 1/2, -z}}, {19, {x, y, z}, {-x + 1/2, -y, 
              z + 1/2}, {-x, y + 1/2, -z + 1/2}}, {20, {x, y, 
              z}, {-x, -y, z + 1/2}, {-x, 
              y, -z + 1/2}, {x + 1/2, y + 1/2, z}}, {21, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {x + 1/2, 
              y + 1/2, z}}, {22, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}, {x, y + 1/2, z + 1/2}, {x + 1/2, y, 
              z + 1/2}}, {23, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}, {x + 1/2, y + 1/2, z + 1/2}}, {24, {x, y, 
              z}, {-x + 1/2, -y, z + 1/2}, {-x, 
              y + 1/2, -z + 1/2}, {x + 1/2, y + 1/2, z + 1/2}}, {25, {x, 
              y, z}, {-x, -y, z}, {x, -y, z}}, {26, {x, y, 
              z}, {-x, -y, z + 1/2}, {x, -y, z + 1/2}}, {27, {x, 
              y, z}, {-x, -y, z}, {x, -y, z + 1/2}}, {28, {x, y, 
              z}, {-x, -y, z}, {x + 1/2, -y, z}}, {29, {x, y, 
              z}, {-x, -y, z + 1/2}, {x + 1/2, -y, z}}, {30, {x, 
              y, z}, {-x, -y, z}, {x, -y + 1/2, 
              z + 1/2}}, {31, {x, y, z}, {-x + 1/2, -y, 
              z + 1/2}, {x + 1/2, -y, z + 1/2}}, {32, {x, y, 
              z}, {-x, -y, z}, {x + 1/2, -y + 1/2, z}}, {33, {x, 
              y, z}, {-x, -y, z + 1/2}, {x + 1/2, -y + 1/2, 
              z}}, {34, {x, y, z}, {-x, -y, 
              z}, {x + 1/2, -y + 1/2, z + 1/2}}, {35, {x, y, 
              z}, {-x, -y, z}, {x, -y, z}, {x + 1/2, y + 1/2, 
              z}}, {36, {x, y, z}, {-x, -y, z + 1/2}, {x, -y, 
              z + 1/2}, {x + 1/2, y + 1/2, z}}, {37, {x, y, 
              z}, {-x, -y, z}, {x, -y, z + 1/2}, {x + 1/2, 
              y + 1/2, z}}, {38, {x, y, z}, {-x, -y, z}, {x, -y, 
              z}, {x, y + 1/2, z + 1/2}}, {39, {x, y, z}, {-x, -y, 
              z}, {x, -y + 1/2, z}, {x, y + 1/2, z + 1/2}}, {40, {x, y, 
              z}, {-x, -y, z}, {x + 1/2, -y, z}, {x, y + 1/2, 
              z + 1/2}}, {41, {x, y, z}, {-x, -y, 
              z}, {x + 1/2, -y + 1/2, z}, {x, y + 1/2, 
              z + 1/2}}, {42, {x, y, z}, {-x, -y, z}, {x, -y, 
              z}, {x, y + 1/2, z + 1/2}, {x + 1/2, y, z + 1/2}}, {43, {x, y, 
              z}, {-x, -y, z}, {x + 1/4, -y + 1/4, z + 1/4}, {x, 
              y + 1/2, z + 1/2}, {x + 1/2, y, z + 1/2}}, {44, {x, y, 
              z}, {-x, -y, z}, {x, -y, z}, {x + 1/2, y + 1/2, 
              z + 1/2}}, {45, {x, y, z}, {-x, -y, 
              z}, {x + 1/2, -y + 1/2, z}, {x + 1/2, y + 1/2, 
              z + 1/2}}, {46, {x, y, z}, {-x, -y, 
              z}, {x + 1/2, -y, z}, {x + 1/2, y + 1/2, 
              z + 1/2}}, {47, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}, {-x, -y, -z}}, {48, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x + 1/2, 
              y, -z + 1/2}, {-x, -y, -z}}, {49, {x, y, 
              z}, {-x, -y, z}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}}, {50, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x + 1/2, 
              y, -z}, {-x, -y, -z}}, {51, {x, y, 
              z}, {-x + 1/2, -y, z}, {-x, 
              y, -z}, {-x, -y, -z}}, {52, {x, y, 
              z}, {-x + 1/2, -y, z}, {-x + 1/2, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {53, {x, y, 
              z}, {-x + 1/2, -y, z + 1/2}, {-x + 1/2, 
              y, -z + 1/2}, {-x, -y, -z}}, {54, {x, y, 
              z}, {-x + 1/2, -y, z}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}}, {55, {x, y, 
              z}, {-x, -y, z}, {-x + 1/2, 
              y + 1/2, -z}, {-x, -y, -z}}, {56, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {57, {x, y, 
              z}, {-x, -y, z + 1/2}, {-x, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {58, {x, y, 
              z}, {-x, -y, z}, {-x + 1/2, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {59, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x, 
              y + 1/2, -z}, {-x, -y, -z}}, {60, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z + 1/2}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}}, {61, {x, y, 
              z}, {-x + 1/2, -y, z + 1/2}, {-x, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}}, {62, {x, y, 
              z}, {-x + 1/2, -y, z + 1/2}, {-x + 1/2, -y, 
              z + 1/2}, {-x, -y, -z}}, {63, {x, y, 
              z}, {-x, -y, z + 1/2}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
              z}}, {64, {x, y, z}, {-x, -y + 1/2, z + 1/2}, {-x, 
              y + 1/2, -z + 1/2}, {-x, -y, -z}, {x + 1/2, 
              y + 1/2, z}}, {65, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
              z}}, {66, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z + 1/2}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
              z}}, {67, {x, y, z}, {-x, -y + 1/2, z}, {-x, 
              y + 1/2, -z}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
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              z + 1/2}, {x + 1/2, y, z + 1/2}}, {217, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, y}, {y, x, 
              z}, {x + 1/2, y + 1/2, z + 1/2}}, {218, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, 
              y}, {y + 1/2, x + 1/2, z + 1/2}}, {219, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, 
              y}, {y + 1/2, x + 1/2, z + 1/2}, {x, y + 1/2, 
              z + 1/2}, {x + 1/2, y, z + 1/2}}, {220, {x, y, 
              z}, {-x + 1/2, -y, z + 1/2}, {-x, 
              y + 1/2, -z + 1/2}, {z, x, y}, {y + 1/4, x + 1/4, 
              z + 1/4}, {x + 1/2, y + 1/2, z + 1/2}}, {221, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, y}, {y, 
              x, -z}, {-x, -y, -z}}, {222, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x + 1/2, 
              y, -z + 1/2}, {z, x, y}, {y, 
              x, -z + 1/2}, {-x, -y, -z}}, {223, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, 
              y}, {y + 1/2, 
              x + 1/2, -z + 1/2}, {-x, -y, -z}}, {224, {x, y, 
              z}, {-x + 1/2, -y + 1/2, z}, {-x + 1/2, 
              y, -z + 1/2}, {z, x, y}, {y + 1/2, 
              x + 1/2, -z}, {-x, -y, -z}}, {225, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, y}, {y, 
              x, -z}, {-x, -y, -z}, {x + 1/2, y, 
              z + 1/2}}, {226, {x, y, z}, {-x, -y, z}, {-x, 
              y, -z}, {z, x, y}, {y + 1/2, 
              x + 1/2, -z + 1/2}, {-x, -y, -z}, {x, y + 1/2, 
              z + 1/2}, {x + 1/2, y, z + 1/2}}, {227, {x, y, 
              z}, {-x + 3/4, -y + 1/4, z + 1/2}, {-x + 1/4, 
              y + 1/2, -z + 3/4}, {z, x, y}, {y + 3/4, 
              x + 1/4, -z + 1/2}, {-x, -y, -z}, {x, y + 1/2, 
              z + 1/2}, {x + 1/2, y, z + 1/2}}, {228, {x, y, 
              z}, {-x + 1/4, -y + 3/4, z + 1/2}, {-x + 3/4, 
              y + 1/2, -z + 1/4}, {z, x, 
              y}, {-x, -y, -z}, {x, y + 1/2, z + 1/2}, {x, 
              y + 1/2, z + 1/2}, {x + 1/2, y, z + 1/2}}, {229, {x, y, 
              z}, {-x, -y, z}, {-x, y, -z}, {z, x, y}, {y, 
              x, -z}, {-x, -y, -z}, {x + 1/2, y + 1/2, 
              z + 1/2}}, {230, {x, y, z}, {-x + 1/2, -y, 
              z + 1/2}, {-x, y + 1/2, -z + 1/2}, {z, x, y}, {y + 3/4, 
              x + 1/4, -z + 1/4}, {-x, -y, -z}, {x + 1/2, 
              y + 1/2, z + 1/2}}};

Space Group Operations for General Positions

\(\(\( (*The\ first\ element\ of\ the\ list\ for\ each\ group\ is\ the\ space\ group\ number\ with\ its\ Hermann - 
        Mauguin\ \(\(notation\)\(.\)\)*) \)\(
\)\(SpaceGroupOperations = {{"1 (P1)", {x, y, z}}, {"2 (P-1)", {x, y, 
              z}, {\(-x\), \(-y\), \(-z\)}}, {"3 (P2)", {x, y, 
              z}, {\(-x\), y, \(-z\)}}, {"4 (P21)", {x, y, z}, {\(-x\), 
              y + 1/2, \(-z\)}}, {"5 (C2)", {x, y, z}, {\(-x\), 
              y, \(-z\)}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}}, {"6 (Pm)", {x, y, z}, {x, \(-y\), 
              z}}, {"7 (Pc)", {x, y, z}, {x, \(-y\), 
              z + 1/2}}, {"8 (Cm)", {x, y, z}, {x, \(-y\), z}, {x + 1/2, 
              y + 1/2, z}, {x + 1/2, \(-y\) + 1/2, z}}, {"9 (Cc)", {x, y, 
              z}, {x, \(-y\), z + 1/2}, {x + 1/2, y + 1/2, 
              z}, {x + 1/2, \(-y\) + 1/2, z + 1/2}}, {"10 (P2/m)", {x, y, 
              z}, {\(-x\), y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\), 
              z}}, {"11 (P21/m)", {x, y, z}, {\(-x\), 
              y + 1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\) + 1/2, 
              z}}, 
{"12 (C2/m)", {x, y, z}, {\(-x\), 
              y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\), z}, {x + 1/2, 
              y + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 
                1/2, \(-y\) + 1/2, z}}, {"13 (P2/c)", {x, y, z}, {\(-x\), 
              y, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\), 
              z + 1/2}}, {"14 (P21/c)", {x, y, z}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\) + 
                1/2, z + 1/2}}, {"15 (C2/c)", {x, y, z}, {\(-x\), 
              y, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x, \(-y\), 
              z + 1/2}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {\(-x\) + 1/2, \(-y\) + 
                1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}}, {"16 (P222)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}}, {"17 (P2221)", {x, y, 
              z}, {\(-x\), \(-y\), z + 1/2}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\)}}, {"18 (P21212)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}}, {"19 (P212121)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}}, {"20 (C2221)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\)}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}}, {"21 (C222)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}}, {"22 (F222)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 
                1/2, y, z + 1/2}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}}, {"23 (I222)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}}, {"24 (I212121)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 
                1/2, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}}, {"25 (Pmm2)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {x, \(-y\), z}, {\(-x\), y, 
              z}}, {"26 (Pmc21)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z}}, {"27 (Pcc2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}}, {"28 (Pma2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x + 1/2, \(-y\), z}, {\(-x\) + 1/2, y, 
              z}}, {"29 (Pca21)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {x + 1/2, \(-y\), z}, {\(-x\) + 1/2, y, 
              z + 1/2}}, {"30 (Pnc2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}}, {"31 (Pmn21)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y, 
              z}}, {"32 (Pba2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}}, {"33 (Pna21)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"34 (Pnn2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"35 (Cmm2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), z}, {\(-x\), y, z}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, z}}, {"36 (Cmc21)", {x, y, 
              z}, {\(-x\), \(-y\), z + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), 
              y, z}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"37 (Ccc2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), z + 1/2}, {\(-x\), y, z + 1/2}, {x + 1/2, 
              y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"38 (Amm2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), z}, {\(-x\), y, z}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {x, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\), y + 1/2, z + 1/2}}, {"39 (Abm2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x, \(-y\) + 1/2, z}, {\(-x\), 
              y + 1/2, z}, {x, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}}, {"40 (Ama2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x + 1/2, \(-y\), z}, {\(-x\) + 1/2, y, z}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}}, {"41 (Aba2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, z}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {x + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, y, z + 1/2}}, {"42 (Fmm2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x, \(-y\), z}, {\(-x\), y, z}, {x, 
              y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}, {x + 1/2, y, z + 1/2}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}}, {"43 (Fdd2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x + 1/4, \(-y\) + 1/4, z + 1/4}, {\(-x\) + 1/4, y + 1/4, 
              z + 1/4}, {x, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z + 1/2}, {x + 1/4, \(-y\) + 3/4, z + 3/4}, {\(-x\) + 1/4, 
              y + 3/4, z + 3/4}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {x + 3/4, \(-y\) + 1/4, z + 3/4}, {\(-x\) + 3/4, 
              y + 1/4, z + 3/4}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {x + 3/4, \(-y\) + 3/4, 
              z + 1/4}, {\(-x\) + 3/4, y + 3/4, 
              z + 1/4}}, {"44 (Imm2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {x, \(-y\), z}, {\(-x\), y, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}}, {"45 (Iba2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}}, {"46 (Ima2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {x + 1/2, \(-y\), z}, {\(-x\) + 1/2, 
              y, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}}, {"47 (Pmmm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, 
              z}}, {"48 (Pnnn)", {x, y, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}}, {"49 (Pccm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}}, {"50 (Pban)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z}, {\(-x\), y + 1/2, 
              z}}, {"51 (Pmma)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z}, {\(-x\), 
              y, \(-z\)}, {x + 
                1/2, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\) + 1/2, y, 
              z}}, {"52 (Pnna)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}}, {"53 (Pmna)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 
                1/2}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 
                1/2, y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y, z}}, {"54 (Pcca)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z}, {\(-x\), 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\)}, {x, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}}, {"55 (Pbam)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}}, {"56 (Pccn)", {x, y, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}}, {"57 (Pbcm)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), y + 1/2, 
              z}}, {"58 (Pnnm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}}, {"59 (Pmmn)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\), 
              y + 1/2, \(-z\)}, {x + 
                1/2, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y, 
              z}}, {"60 (Pbcn)", {x, y, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\), 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"61 (Pbca)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"62 (Pnma)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"63 (Cmcm)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-x\), 
              y, \(-z\) + 
                1/2}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\) + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, z}}, {"64 (Cmca)", {x, y, 
              z}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 
                1/2}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), y, 
              z}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"65 (Cmmm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, z}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"66 (Cccm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"67 (Cmma)", {x, y, z}, {\(-x\), \(-y\) + 1/2, 
              z}, {\(-x\), 
              y + 1/2, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z}, {\(-x\), y, 
              z}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\), 
              z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y, \(-z\)}, {x + 1/2, \(-y\), z}, {\(-x\) + 1/2, y + 1/2, 
              z}}, {"68 (Ccca)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z}, {\(-x\), 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\)}, {x, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {x + 1/2, y + 1/2, z}, {\(-x\), \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, z + 1/2}}, {"69 (Fmmm)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, z}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, z + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {\(-x\) + 
                1/2, \(-y\), \(-z\) + 1/2}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, z}}, {"70 (Fddd)", {x, y, 
              z}, {\(-x\) + 3/4, \(-y\) + 3/4, z}, {\(-x\) + 3/4, 
              y, \(-z\) + 3/4}, {x, \(-y\) + 3/4, \(-z\) + 
                3/4}, {\(-x\), \(-y\), \(-z\)}, {x + 1/4, 
              y + 1/4, \(-z\)}, {x + 1/4, \(-y\), z + 1/4}, {\(-x\), y + 1/4, 
              z + 1/4}, {x, y + 1/2, z + 1/2}, {\(-x\) + 3/4, \(-y\) + 1/4, 
              z + 1/2}, {\(-x\) + 3/4, 
              y + 1/2, \(-z\) + 1/4}, {x, \(-y\) + 1/4, \(-z\) + 
                1/4}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/4, 
              y + 3/4, \(-z\) + 1/2}, {x + 1/4, \(-y\) + 1/2, 
              z + 3/4}, {\(-x\), y + 3/4, z + 3/4}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/4, \(-y\) + 3/4, z + 1/2}, {\(-x\) + 1/4, 
              y, \(-z\) + 1/4}, {x + 1/2, \(-y\) + 3/4, \(-z\) + 
                1/4}, {\(-x\) + 1/2, \(-y\), \(-z\) + 1/2}, {x + 3/4, 
              y + 1/4, \(-z\) + 1/2}, {x + 3/4, \(-y\), 
              z + 3/4}, {\(-x\) + 1/2, y + 1/4, z + 3/4}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/4, \(-y\) + 1/4, z}, {\(-x\) + 1/4, 
              y + 1/2, \(-z\) + 3/4}, {x + 1/2, \(-y\) + 1/4, \(-z\) + 
                3/4}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 3/4, 
              y + 3/4, \(-z\)}, {x + 3/4, \(-y\) + 1/2, 
              z + 1/4}, {\(-x\) + 1/2, y + 3/4, 
              z + 1/4}}, {"71 (Immm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}}, {"72 (Ibam)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 1/2}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}}, {"73 (Ibca)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {\(-x\) + 1/2, \(-y\) + 
                1/2, \(-z\) + 1/2}, {x, y + 1/2, \(-z\)}, {x + 1/2, \(-y\), 
              z}, {\(-x\), y, z + 1/2}}, {"74 (Imma)", {x, y, 
              z}, {\(-x\), \(-y\) + 1/2, z}, {\(-x\), 
              y + 1/2, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z}, {\(-x\), y, 
              z}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}}, {"75 (P4)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}}, {"76 (P41)", {x, y, 
              z}, {\(-x\), \(-y\), z + 1/2}, {\(-y\), x, 
              z + 1/4}, {y, \(-x\), z + 3/4}}, {"77 (P42)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z + 1/2}, {y, \(-x\), 
              z + 1/2}}, {"78 (P43)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-y\), x, z + 3/4}, {y, \(-x\), 
              z + 1/4}}, {"79 (I4)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}}, {"80 (I41)", \ {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\), x + 1/2, 
              z + 1/4}, {y + 1/2, \(-x\), z + 3/4}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x, 
              z + 3/4}, {y, \(-x\) + 1/2, 
              z + 1/4}}, 
{"81 (P-4)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}}, {"82 (I-4)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}}, {"83 (P4/m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}}, {"84 (P42/m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), 
              z + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}}, {"85 (P4/n)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z}, {y, \(-x\) + 1/2, z}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\), 
              x + 1/2, \(-z\)}}, {"86 (P42/n)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\), x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\), 
              z + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 
                1/2, x, \(-z\) + 1/2}}, {"87 (I4/m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}}, {"88 (I41/a)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-y\) + 3/4, x + 1/4, 
              z + 1/4}, {y + 3/4, \(-x\) + 3/4, 
              z + 3/4}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {y + 1/4, \(-x\) + 3/4, \(-z\) + 
                3/4}, {\(-y\) + 1/4, x + 1/4, \(-z\) + 1/4}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-y\) + 1/4, 
              x + 3/4, z + 3/4}, {y + 1/4, \(-x\) + 1/4, 
              z + 1/4}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\)}, {y + 3/4, \(-x\) + 1/4, \(-z\) + 
                1/4}, {\(-y\) + 3/4, 
              x + 3/4, \(-z\) + 3/4}}, {"89 (P422)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}}, {"90 (P4212)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x + 1/2, 
              z}, {y + 1/2, \(-x\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}}, {"91 (P4122)", {x, 
              y, z}, {\(-x\), \(-y\), z + 1/2}, {\(-y\), x, 
              z + 1/4}, {y, \(-x\), z + 3/4}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {y, 
              x, \(-z\) + 3/4}, {\(-y\), \(-x\), \(-z\) + 
                1/4}}, {"92 (P41212)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/4}, {y + 1/2, \(-x\) + 1/2, z + 3/4}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/4}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                3/4}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\) + 
                1/2}}, {"93 (P4222)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), z + 1/2}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}}, {"94 (P42212)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\) + 1/2, x + 1/2, z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}}, {"95 (P4322)", {x, 
              y, z}, {\(-x\), \(-y\), z + 1/2}, {\(-y\), x, 
              z + 3/4}, {y, \(-x\), z + 1/4}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {y, 
              x, \(-z\) + 1/4}, {\(-y\), \(-x\), \(-z\) + 
                3/4}}, {"96 (P43212)", {x, y, z}, {\(-x\), \(-y\), 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 3/4}, {y + 1/2, \(-x\) + 1/2, z + 1/4}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 3/4}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/4}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\) + 
                1/2}}, {"97 (I422)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}}, {"98 (I4122)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\), x + 1/2, 
              z + 1/4}, {y + 1/2, \(-x\), z + 3/4}, {\(-x\) + 1/2, 
              y, \(-z\) + 3/4}, {x, \(-y\) + 1/2, \(-z\) + 1/4}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\)}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x, 
              z + 3/4}, {y, \(-x\) + 1/2, z + 1/4}, {\(-x\), 
              y + 1/2, \(-z\) + 1/4}, {x + 1/2, \(-y\), \(-z\) + 3/4}, {y, 
              x, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}}, {"99 (P4mm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-y\), \(-x\), z}, {y, x, z}}, {"100 (P4bm)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y + 1/2, x + 1/2, 
              z}}, {"101 (P42cm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), z + 1/2}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"102 (P42nm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\) + 1/2, x + 1/2, z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"103 (P4cc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {y, 
              x, z + 1/2}}, {"104 (P4nc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}}, {"105 (P42mc)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z + 1/2}, {y, \(-x\), 
              z + 1/2}, {x, \(-y\), z}, {\(-x\), y, z}, {\(-y\), \(-x\), 
              z + 1/2}, {y, x, z + 1/2}}, {"106 (P42bc)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z + 1/2}, {y, \(-x\), 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, x + 1/2, 
              z + 1/2}}, {"107 (I4mm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-y\), \(-x\), z}, {y, x, z}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, x + 1/2, z + 1/2}}, {"108 (I4cm)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {y, x, z + 1/2}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y + 1/2, x + 1/2, 
              z}}, {"109 (I41md)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\), x + 1/2, 
              z + 1/4}, {y + 1/2, \(-x\), z + 3/4}, {x, \(-y\), 
              z}, {\(-x\) + 1/2, y + 1/2, z + 1/2}, {\(-y\), \(-x\) + 1/2, 
              z + 1/4}, {y + 1/2, x, z + 3/4}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x, 
              z + 3/4}, {y, \(-x\) + 1/2, z + 1/4}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\), y, z}, {\(-y\) + 1/2, \(-x\), z + 3/4}, {y, 
              x + 1/2, z + 1/4}}, {"110 (I41cd)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-y\), x + 1/2, 
              z + 1/4}, {y + 1/2, \(-x\), z + 3/4}, {x, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, z}, {\(-y\), \(-x\) + 1/2, 
              z + 3/4}, {y + 1/2, x, z + 1/4}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x, 
              z + 3/4}, {y, \(-x\) + 1/2, z + 1/4}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\), y, z + 1/2}, {\(-y\) + 1/2, \(-x\), z + 1/4}, {y, 
              x + 1/2, z + 3/4}}, {"111 (P-42m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"112 (P-42c)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 1/2}, {\(-y\), \(-x\), 
              z + 1/2}, {y, x, z + 1/2}}, {"113 (P-421m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {\(-y\) + 
                1/2, \(-x\) + 1/2, z}, {y + 1/2, x + 1/2, 
              z}}, {"114 (P-421c)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}}, {"115 (P-4m2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, z}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}}, {"116 (P-4c2)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x, \(-y\), z + 1/2}, {\(-x\), y, z + 1/2}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}}, {"117 (P-4b2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}}, {"118 (P-4n2)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}}, {"119 (I-4m2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}}, {"120 (I-4c2)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x, \(-y\), 
              z + 1/2}, {\(-x\), y, z + 1/2}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, z}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}}, {"121 (I-42m)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {\(-y\), \(-x\), z}, {y, x, 
              z}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}}, {"122 (I-42d)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {\(-x\) + 1/2, 
              y, \(-z\) + 3/4}, {x + 1/2, \(-y\), \(-z\) + 3/4}, {\(-y\) + 
                1/2, \(-x\), z + 3/4}, {y + 1/2, x, z + 3/4}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/4}, {x, \(-y\) + 1/2, \(-z\) + 
                1/4}, {\(-y\), \(-x\) + 1/2, z + 1/4}, {y, x + 1/2, 
              z + 1/4}}, {"123 (P4/mmm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"124 (P4/mcc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 1/2}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {y, x, 
              z + 1/2}}, {"125 (P4/nbm)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z}, {y, \(-x\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\) + 1/2, \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\), 
              x + 1/2, \(-z\)}, {x + 1/2, \(-y\), z}, {\(-x\), y + 1/2, 
              z}, {\(-y\), \(-x\), z}, {y + 1/2, x + 1/2, 
              z}}, {"126 (P4/nnc)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z}, {y, \(-x\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {y, 
              x, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\), 
              x + 1/2, \(-z\)}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {y + 1/2, x + 1/2, 
              z + 1/2}}, {"127 (P4/mbm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y + 1/2, x + 1/2, 
              z}}, {"128 (P4/mnc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, x + 1/2, 
              z + 1/2}}, {"129 (P4/nmm)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z}, {y, \(-x\) + 1/2, z}, {\(-x\), 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), \(-z\)}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\), 
              x + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y, x, 
              z}}, {"130 (P4/ncc)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z}, {y, \(-x\) + 1/2, z}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {y + 
                1/2, x + 1/2, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\), 
              x + 1/2, \(-z\)}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y, x, 
              z + 1/2}}, {"131 (P42/mmc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), z + 1/2}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-y\), \(-x\), z + 1/2}, {y, x, 
              z + 1/2}}, {"132 (P42/mcm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), z + 1/2}, {\(-x\), 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 1/2}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {y, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}, {\(-y\), \(-x\), z}, {y, x, 
              z}}, {"133 (P42/nbc)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z + 1/2}, {y, \(-x\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\) + 1/2, \(-z\)}, {y, 
              x, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\), z}, {\(-x\), y + 1/2, 
              z}, {\(-y\), \(-x\), z + 1/2}, {y + 1/2, x + 1/2, 
              z + 1/2}}, {"134 (P42/nnm)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z + 1/2}, {y, \(-x\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {y, 
              x, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, z + 1/2}, {\(-y\), \(-x\), z}, {y + 1/2, x + 1/2, 
              z}}, {"135 (P42/mbc)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z + 1/2}, {y, \(-x\), z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, z}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}}, {"136 (P42/mnm)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, z + 1/2}, {\(-y\), \(-x\), 
              z}, {y, x, z}}, {"137 (P42/nmc)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z + 1/2}, {y, \(-x\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), \(-z\)}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z}, {\(-x\) + 1/2, y, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y, x, 
              z + 1/2}}, {"138 (P42/ncm)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-y\) + 1/2, x, 
              z + 1/2}, {y, \(-x\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {y + 
                1/2, x + 
                1/2, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, y + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y, x, 
              z}}, {"139 (I4/mmm)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-y\), x, z}, {y, \(-x\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), x, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-y\), \(-x\), z}, {y, x, z}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, z + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}}, {"140 (I4/mcm)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-y\), x, z}, {y, \(-x\), 
              z}, {\(-x\), y, \(-z\) + 1/2}, {x, \(-y\), \(-z\) + 1/2}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x, \(-y\), z + 1/2}, {\(-x\), y, 
              z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {y, x, z + 1/2}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-y\) + 1/2, x + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, z}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z}, {y + 1/2, x + 1/2, z}}, {"141 (I41/amd)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-y\) + 1/4, x + 3/4, 
              z + 1/4}, {y + 1/4, \(-x\) + 1/4, z + 3/4}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\), \(-z\)}, {y + 1/4, 
              x + 3/4, \(-z\) + 1/4}, {\(-y\) + 1/4, \(-x\) + 1/4, \(-z\) + 
                3/4}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {y + 3/4, \(-x\) + 1/4, \(-z\) + 
                3/4}, {\(-y\) + 3/4, 
              x + 3/4, \(-z\) + 1/4}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y, 
              z}, {\(-y\) + 3/4, \(-x\) + 1/4, z + 3/4}, {y + 3/4, x + 3/4, 
              z + 1/4}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z}, {\(-y\) + 3/4, x + 1/4, z + 3/4}, {y + 3/4, \(-x\) + 3/4, 
              z + 1/4}, {\(-x\), 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {y + 
                3/4, x + 1/4, \(-z\) + 3/4}, {\(-y\) + 3/4, \(-x\) + 
                3/4, \(-z\) + 1/4}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {x, 
              y + 1/2, \(-z\)}, {y + 1/4, \(-x\) + 3/4, \(-z\) + 
                1/4}, {\(-y\) + 1/4, 
              x + 1/4, \(-z\) + 3/4}, {x, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, z + 1/2}, {\(-y\) + 1/4, \(-x\) + 3/4, 
              z + 1/4}, {y + 1/4, x + 1/4, 
              z + 3/4}}, {"142 (I41/acd)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-y\) + 1/4, x + 3/4, 
              z + 1/4}, {y + 1/4, \(-x\) + 1/4, z + 3/4}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {y + 1/4, 
              x + 3/4, \(-z\) + 3/4}, {\(-y\) + 1/4, \(-x\) + 1/4, \(-z\) + 
                1/4}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {y + 3/4, \(-x\) + 1/4, \(-z\) + 
                3/4}, {\(-y\) + 3/4, 
              x + 3/4, \(-z\) + 1/4}, {x + 1/2, \(-y\), z}, {\(-x\), y, 
              z + 1/2}, {\(-y\) + 3/4, \(-x\) + 1/4, z + 1/4}, {y + 3/4, 
              x + 3/4, z + 3/4}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-y\) + 3/4, x + 1/4, 
              z + 3/4}, {y + 3/4, \(-x\) + 3/4, z + 1/4}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {y + 
                3/4, x + 1/4, \(-z\) + 1/4}, {\(-y\) + 3/4, \(-x\) + 
                3/4, \(-z\) + 3/4}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {x, 
              y + 1/2, \(-z\)}, {y + 1/4, \(-x\) + 3/4, \(-z\) + 
                1/4}, {\(-y\) + 1/4, 
              x + 1/4, \(-z\) + 3/4}, {x, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-y\) + 1/4, \(-x\) + 3/4, z + 3/4}, {y + 1/4, x + 1/4, 
              z + 1/4}}, {"143 (P3)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}}, {"144 (P31)", {x, y, 
              z}, {\(-y\), x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}}, {"145 (P32)", {x, y, z}, {\(-y\), x - y, 
              z + 2/3}, {\(-x\) + y, \(-x\), z + 1/3}}, {"146 (R3)", {x, 
              y, z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {x + 2/3, 
              y + 1/3, z + 1/3}, {\(-y\) + 2/3, x - y + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, z + 1/3}, {x + 1/3, 
              y + 2/3, z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, 
              z + 2/3}}, {"147 (P-3)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - y, 
              x, \(-z\)}}, {"148 (R-3)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - y, 
              x, \(-z\)}, {x + 2/3, y + 1/3, z + 1/3}, {\(-y\) + 2/3, 
              x - y + 1/3, z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {\(-x\) + 2/3, \(-y\) + 1/3, \(-z\) + 1/3}, {y + 
                2/3, \(-x\) + y + 1/3, \(-z\) + 1/3}, {x - y + 2/3, 
              x + 1/3, \(-z\) + 1/3}, {x + 1/3, y + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, 
              z + 2/3}, {\(-x\) + 1/3, \(-y\) + 2/3, \(-z\) + 2/3}, {y + 
                1/3, \(-x\) + y + 2/3, \(-z\) + 2/3}, {x - y + 1/3, 
              x + 2/3, \(-z\) + 2/3}}, {"149 (P312)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}}, {"150 (P321)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}}, {"151 (P3112)", {x, y, z}, {\(-y\), x - y, 
              z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {\(-y\), \(-x\), \(-z\) + 2/3}, {\(-x\) + y, 
              y, \(-z\) + 1/3}, {x, x - y, \(-z\)}}, {"152 (P3121)", {x, 
              y, z}, {\(-y\), x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\) + 2/3}, {\(-x\), \(-x\) + 
                y, \(-z\) + 1/3}}, {"153 (P3212)", {x, y, z}, {\(-y\), 
              x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {\(-y\), \(-x\), \(-z\) + 1/3}, {\(-x\) + y, 
              y, \(-z\) + 2/3}, {x, x - y, \(-z\)}}, {"154 (P3221)", {x, 
              y, z}, {\(-y\), x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\) + 1/3}, {\(-x\), \(-x\) + 
                y, \(-z\) + 2/3}}, {"155 (R32)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {x + 2/3, y + 1/3, z + 1/3}, {\(-y\) + 2/3, 
              x - y + 1/3, z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {y + 2/3, 
              x + 1/3, \(-z\) + 1/3}, {x - y + 2/3, \(-y\) + 1/3, \(-z\) + 
                1/3}, {\(-x\) + 2/3, \(-x\) + y + 1/3, \(-z\) + 1/3}, {x + 
                1/3, y + 2/3, z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, z + 2/3}, {y + 1/3, 
              x + 2/3, \(-z\) + 2/3}, {x - y + 1/3, \(-y\) + 2/3, \(-z\) + 
                2/3}, {\(-x\) + 1/3, \(-x\) + y + 2/3, \(-z\) + 
                2/3}}, {"156 (P3m1)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-y\), \(-x\), z}, {\(-x\) + y, 
              y, z}, {x, x - y, z}}, {"157 (P31m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"158 (P3c1)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, z + 1/2}, {x, 
              x - y, z + 1/2}}, {"159 (P31c)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {y, x, z + 1/2}, {x - y, \(-y\), 
              z + 1/2}, {\(-x\), \(-x\) + y, z + 1/2}}, {"160 (R3m)", {x, 
              y, z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), z}, {\(-x\) + y, y, z}, {x, x - y, 
              z}, {x + 2/3, y + 1/3, z + 1/3}, {\(-y\) + 2/3, x - y + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {\(-y\) + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, y + 1/3, z + 1/3}, {x + 2/3, 
              x - y + 1/3, z + 1/3}, {x + 1/3, y + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, \(-x\) + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, y + 2/3, z + 2/3}, {x + 1/3, 
              x - y + 2/3, z + 2/3}}, {"161 (R3c)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-y\), \(-x\), 
              z + 1/2}, {\(-x\) + y, y, z + 1/2}, {x, x - y, 
              z + 1/2}, {x + 2/3, y + 1/3, z + 1/3}, {\(-y\) + 2/3, 
              x - y + 1/3, z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {\(-y\) + 2/3, \(-x\) + 1/3, 
              z + 5/6}, {\(-x\) + y + 2/3, y + 1/3, z + 5/6}, {x + 2/3, 
              x - y + 1/3, z + 5/6}, {x + 1/3, y + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, \(-x\) + 2/3, 
              z + 1/6}, {\(-x\) + y + 1/3, y + 2/3, z + 1/6}, {x + 1/3, 
              x - y + 2/3, z + 1/6}}, {"162 (P-31m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"163 (P-31c)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-y\), \(-x\), \(-z\) + 1/2}, {\(-x\) + y, 
              y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {y, x, 
              z + 1/2}, {x - y, \(-y\), z + 1/2}, {\(-x\), \(-x\) + y, 
              z + 1/2}}, {"164 (P-3m1)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}}, {"165 (P-3c1)", {x, 
              y, z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\) + 1/2}, {x - y, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-x\) + y, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - 
                y, x, \(-z\)}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, 
              z + 1/2}, {x, x - y, z + 1/2}}, {"166 (R-3m)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}, {x + 2/3, y + 1/3, 
              z + 1/3}, {\(-y\) + 2/3, x - y + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, z + 1/3}, {y + 2/3, 
              x + 1/3, \(-z\) + 1/3}, {x - y + 2/3, \(-y\) + 1/3, \(-z\) + 
                1/3}, {\(-x\) + 2/3, \(-x\) + y + 1/3, \(-z\) + 
                1/3}, {\(-x\) + 2/3, \(-y\) + 1/3, \(-z\) + 1/3}, {y + 
                2/3, \(-x\) + y + 1/3, \(-z\) + 1/3}, {x - y + 2/3, 
              x + 1/3, \(-z\) + 1/3}, {\(-y\) + 2/3, \(-x\) + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, y + 1/3, z + 1/3}, {x + 2/3, 
              x - y + 1/3, z + 1/3}, {x + 1/3, y + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, z + 2/3}, {y + 1/3, 
              x + 2/3, \(-z\) + 2/3}, {x - y + 1/3, \(-y\) + 2/3, \(-z\) + 
                2/3}, {\(-x\) + 1/3, \(-x\) + y + 2/3, \(-z\) + 
                2/3}, {\(-x\) + 1/3, \(-y\) + 2/3, \(-z\) + 2/3}, {y + 
                1/3, \(-x\) + y + 2/3, \(-z\) + 2/3}, {x - y + 1/3, 
              x + 2/3, \(-z\) + 2/3}, {\(-y\) + 1/3, \(-x\) + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, y + 2/3, z + 2/3}, {x + 1/3, 
              x - y + 2/3, z + 2/3}}, {"167 (R-3c)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {y, 
              x, \(-z\) + 1/2}, {x - y, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-x\) + y, \(-z\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - 
                y, x, \(-z\)}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, 
              z + 1/2}, {x, x - y, z + 1/2}, {x + 2/3, y + 1/3, 
              z + 1/3}, {\(-y\) + 2/3, x - y + 1/3, 
              z + 1/3}, {\(-x\) + y + 2/3, \(-x\) + 1/3, z + 1/3}, {y + 2/3, 
              x + 1/3, \(-z\) + 5/6}, {x - y + 2/3, \(-y\) + 1/3, \(-z\) + 
                5/6}, {\(-x\) + 2/3, \(-x\) + y + 1/3, \(-z\) + 
                5/6}, {\(-x\) + 2/3, \(-y\) + 1/3, \(-z\) + 1/3}, {y + 
                2/3, \(-x\) + y + 1/3, \(-z\) + 1/3}, {x - y + 2/3, 
              x + 1/3, \(-z\) + 1/3}, {\(-y\) + 2/3, \(-x\) + 1/3, 
              z + 5/6}, {\(-x\) + y + 2/3, y + 1/3, z + 5/6}, {x + 2/3, 
              x - y + 1/3, z + 5/6}, {x + 1/3, y + 2/3, 
              z + 2/3}, {\(-y\) + 1/3, x - y + 2/3, 
              z + 2/3}, {\(-x\) + y + 1/3, \(-x\) + 2/3, z + 2/3}, {y + 1/3, 
              x + 2/3, \(-z\) + 1/6}, {x - y + 1/3, \(-y\) + 2/3, \(-z\) + 
                1/6}, {\(-x\) + 1/3, \(-x\) + y + 2/3, \(-z\) + 
                1/6}, {\(-x\) + 1/3, \(-y\) + 2/3, \(-z\) + 2/3}, {y + 
                1/3, \(-x\) + y + 2/3, \(-z\) + 2/3}, {x - y + 1/3, 
              x + 2/3, \(-z\) + 2/3}, {\(-y\) + 1/3, \(-x\) + 2/3, 
              z + 1/6}, {\(-x\) + y + 1/3, y + 2/3, z + 1/6}, {x + 1/3, 
              x - y + 2/3, z + 1/6}}, {"168 (P6)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}}, {"169 (P61)", {x, 
              y, z}, {\(-y\), x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 5/6}, {x - y, x, z + 1/6}}, {"170 (P65)", {x, y, 
              z}, {\(-y\), x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 1/6}, {x - y, x, z + 5/6}}, {"171 (P62)", {x, y, 
              z}, {\(-y\), x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, 
              z + 2/3}, {x - y, x, z + 1/3}}, {"172 (P64)", {x, y, 
              z}, {\(-y\), x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, 
              z + 1/3}, {x - y, x, z + 2/3}}, {"173 (P63)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 1/2}, {x - y, x, z + 1/2}}, {"174 (P-6)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {x, 
              y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + 
                y, \(-x\), \(-z\)}}, {"175 (P6/m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, 
              z}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + y, \(-z\)}, {x - y, 
              x, \(-z\)}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + 
                y, \(-x\), \(-z\)}}, {"176 (P63/m)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z + 1/2}, {y, \(-x\) + y, z + 1/2}, {x - y, x, 
              z + 1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, 
              y, \(-z\) + 1/2}, {\(-y\), 
              x - y, \(-z\) + 1/2}, {\(-x\) + y, \(-x\), \(-z\) + 
                1/2}}, {"177 (P622)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, 
              y, \(-z\)}, {x, x - y, \(-z\)}}, {"178 (P6122)", {x, y, 
              z}, {\(-y\), x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 5/6}, {x - y, x, z + 1/6}, {y, 
              x, \(-z\) + 1/3}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\) + 2/3}, {\(-y\), \(-x\), \(-z\) + 5/6}, {\(-x\) + 
                y, y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 1/6}}, {"179 (P6522)", {x, y, z}, {\(-y\), 
              x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 1/6}, {x - y, x, z + 5/6}, {y, 
              x, \(-z\) + 2/3}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\) + 1/3}, {\(-y\), \(-x\), \(-z\) + 1/6}, {\(-x\) + 
                y, y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 5/6}}, {"180 (P6222)", {x, y, z}, {\(-y\), 
              x - y, z + 2/3}, {\(-x\) + y, \(-x\), 
              z + 1/3}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, 
              z + 2/3}, {x - y, x, z + 1/3}, {y, 
              x, \(-z\) + 2/3}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\) + 1/3}, {\(-y\), \(-x\), \(-z\) + 2/3}, {\(-x\) + 
                y, y, \(-z\)}, {x, 
              x - y, \(-z\) + 1/3}}, {"181 (P6422)", {x, y, z}, {\(-y\), 
              x - y, z + 1/3}, {\(-x\) + y, \(-x\), 
              z + 2/3}, {\(-x\), \(-y\), z}, {y, \(-x\) + y, 
              z + 1/3}, {x - y, x, z + 2/3}, {y, 
              x, \(-z\) + 1/3}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\) + 2/3}, {\(-y\), \(-x\), \(-z\) + 1/3}, {\(-x\) + 
                y, y, \(-z\)}, {x, 
              x - y, \(-z\) + 2/3}}, {"182 (P6322)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z + 1/2}, {y, \(-x\) + y, z + 1/2}, {x - y, x, z + 1/2}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\) + 1/2}, {\(-x\) + y, 
              y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 1/2}}, {"183 (P6mm)", {x, y, z}, {\(-y\), 
              x - y, z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}, {y, x, 
              z}, {x - y, \(-y\), z}, {\(-x\), \(-x\) + y, 
              z}}, {"184 (P6cc)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {\(-y\), \(-x\), 
              z + 1/2}, {\(-x\) + y, y, z + 1/2}, {x, x - y, z + 1/2}, {y, x, 
              z + 1/2}, {x - y, \(-y\), z + 1/2}, {\(-x\), \(-x\) + y, 
              z + 1/2}}, {"185 (P63cm)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z + 1/2}, {y, \(-x\) + y, z + 1/2}, {x - y, x, 
              z + 1/2}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, 
              z + 1/2}, {x, x - y, z + 1/2}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"186 (P63mc)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 1/2}, {x - y, x, z + 1/2}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}, {y, x, 
              z + 1/2}, {x - y, \(-y\), z + 1/2}, {\(-x\), \(-x\) + y, 
              z + 1/2}}, {"187 (P-6m2)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, 
              z}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}}, {"188 (P-6c2)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {x, y, \(-z\) + 1/2}, {\(-y\), 
              x - y, \(-z\) + 1/2}, {\(-x\) + y, \(-x\), \(-z\) + 
                1/2}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, 
              z + 1/2}, {x, x - y, 
              z + 1/2}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, 
              y, \(-z\)}, {x, x - y, \(-z\)}}, {"189 (P-62m)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {x, 
              y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"190 (P-62c)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), z}, {x, 
              y, \(-z\) + 1/2}, {\(-y\), 
              x - y, \(-z\) + 1/2}, {\(-x\) + y, \(-x\), \(-z\) + 1/2}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {y, x, z + 1/2}, {x - y, \(-y\), 
              z + 1/2}, {\(-x\), \(-x\) + y, 
              z + 1/2}}, {"191 (P6/mmm)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, 
              y, \(-z\)}, {x, 
              x - y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {\(-y\), \(-x\), 
              z}, {\(-x\) + y, y, z}, {x, x - y, z}, {y, x, 
              z}, {x - y, \(-y\), z}, {\(-x\), \(-x\) + y, 
              z}}, {"192 (P6/mcc)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z}, {y, \(-x\) + y, z}, {x - y, x, z}, {y, 
              x, \(-z\) + 1/2}, {x - y, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-x\) + y, \(-z\) + 
                1/2}, {\(-y\), \(-x\), \(-z\) + 1/2}, {\(-x\) + y, 
              y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, y, \(-z\)}, {\(-y\), 
              x - y, \(-z\)}, {\(-x\) + y, \(-x\), \(-z\)}, {\(-y\), \(-x\), 
              z + 1/2}, {\(-x\) + y, y, z + 1/2}, {x, x - y, z + 1/2}, {y, x, 
              z + 1/2}, {x - y, \(-y\), z + 1/2}, {\(-x\), \(-x\) + y, 
              z + 1/2}}, {"193 (P63/mcm)", {x, y, z}, {\(-y\), x - y, 
              z}, {\(-x\) + y, \(-x\), z}, {\(-x\), \(-y\), 
              z + 1/2}, {y, \(-x\) + y, z + 1/2}, {x - y, x, z + 1/2}, {y, 
              x, \(-z\) + 1/2}, {x - y, \(-y\), \(-z\) + 
                1/2}, {\(-x\), \(-x\) + y, \(-z\) + 
                1/2}, {\(-y\), \(-x\), \(-z\)}, {\(-x\) + y, y, \(-z\)}, {x, 
              x - y, \(-z\)}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, 
              y, \(-z\) + 1/2}, {\(-y\), 
              x - y, \(-z\) + 1/2}, {\(-x\) + y, \(-x\), \(-z\) + 
                1/2}, {\(-y\), \(-x\), z + 1/2}, {\(-x\) + y, y, 
              z + 1/2}, {x, x - y, z + 1/2}, {y, x, z}, {x - y, \(-y\), 
              z}, {\(-x\), \(-x\) + y, z}}, {"194 (P63/mmc)", {x, y, 
              z}, {\(-y\), x - y, z}, {\(-x\) + y, \(-x\), 
              z}, {\(-x\), \(-y\), z + 1/2}, {y, \(-x\) + y, 
              z + 1/2}, {x - y, x, z + 1/2}, {y, 
              x, \(-z\)}, {x - y, \(-y\), \(-z\)}, {\(-x\), \(-x\) + 
                y, \(-z\)}, {\(-y\), \(-x\), \(-z\) + 1/2}, {\(-x\) + y, 
              y, \(-z\) + 1/2}, {x, 
              x - y, \(-z\) + 1/2}, {\(-x\), \(-y\), \(-z\)}, {y, \(-x\) + 
                y, \(-z\)}, {x - y, x, \(-z\)}, {x, 
              y, \(-z\) + 1/2}, {\(-y\), 
              x - y, \(-z\) + 1/2}, {\(-x\) + y, \(-x\), \(-z\) + 
                1/2}, {\(-y\), \(-x\), z}, {\(-x\) + y, y, z}, {x, x - y, 
              z}, {y, x, z + 1/2}, {x - y, \(-y\), 
              z + 1/2}, {\(-x\), \(-x\) + y, z + 1/2}}, {"195 (P23)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}}, {"196 (F23)", {x, y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {x, 
              y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), \(-x\) + 
                1/2, y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z + 1/2, 
              x + 1/2}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\), \(-z\) + 1/2, x + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {z + 1/2, x, 
              y + 1/2}, {z + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\), y + 1/2}, {\(-z\) + 1/2, 
              x, \(-y\) + 1/2}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y + 1/2, \(-z\), \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), x + 1/2}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}}, {"197 (I23)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\) + 1/2, y + 1/2}, {\(-z\) + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, 
              x + 1/2}}, {"198 (P213)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), 
              x + 1/2}}, {"199 (I213)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {x + 1/2, 
              y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z, \(-x\), \(-y\) + 1/2}, {\(-z\), \(-x\) + 1/2, 
              y}, {\(-z\) + 1/2, x, \(-y\)}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\)}, {y, \(-z\), \(-x\) + 1/2}, {\(-y\), \(-z\) + 1/2, 
              x}}, {"200 (Pm-3)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}}, {"201 (Pn-3)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, x, 
              y}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x, \(-y\) + 1/2}, {y, z, 
              x}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x + 1/2, 
              y + 1/2}, {z + 1/2, x + 1/2, \(-y\)}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y + 1/2, \(-z\), 
              x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y + 1/2, 
              z + 1/2, \(-x\)}}, {"202 (Fm-3)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), \(-x\) + 
                1/2, y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z + 1/2, 
              x + 1/2}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\), \(-z\) + 1/2, 
              x + 1/2}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x + 1/2, y + 1/2}, {z, 
              x + 1/2, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 
                1/2, x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y, 
              z + 1/2, \(-x\) + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {z + 1/2, x, 
              y + 1/2}, {z + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\), y + 1/2}, {\(-z\) + 1/2, 
              x, \(-y\) + 1/2}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y + 1/2, \(-z\), \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), 
              x + 1/2}, {\(-x\) + 1/2, \(-y\), \(-z\) + 1/2}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x, y + 1/2}, {z + 1/2, x, \(-y\) + 1/2}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\) + 1/2, \(-z\), \(-x\) + 1/2}, {y + 
                1/2, \(-z\), x + 1/2}, {\(-y\) + 1/2, z, x + 1/2}, {y + 1/2, 
              z, \(-x\) + 1/2}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, 
              x}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, 
              z}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, 
              x + 1/2, y}, {z + 1/2, 
              x + 1/2, \(-y\)}, {z + 1/2, \(-x\) + 1/2, 
              y}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 
                1/2, x}, {\(-y\) + 1/2, z + 1/2, x}, {y + 1/2, 
              z + 1/2, \(-x\)}}, {"203 (Fd-3)", {x, y, 
              z}, {\(-x\) + 1/4, \(-y\) + 1/4, z}, {\(-x\) + 1/4, 
              y, \(-z\) + 1/4}, {x, \(-y\) + 1/4, \(-z\) + 1/4}, {z, x, 
              y}, {z, \(-x\) + 1/4, \(-y\) + 1/4}, {\(-z\) + 1/4, \(-x\) + 
                1/4, y}, {\(-z\) + 1/4, x, \(-y\) + 1/4}, {y, z, 
              x}, {\(-y\) + 1/4, 
              z, \(-x\) + 1/4}, {y, \(-z\) + 1/4, \(-x\) + 1/4}, {\(-y\) + 
                1/4, \(-z\) + 1/4, x}, {\(-x\), \(-y\), \(-z\)}, {x + 3/4, 
              y + 3/4, \(-z\)}, {x + 3/4, \(-y\), z + 3/4}, {\(-x\), y + 3/4, 
              z + 3/4}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x + 3/4, 
              y + 3/4}, {z + 3/4, x + 3/4, \(-y\)}, {z + 3/4, \(-x\), 
              y + 3/4}, {\(-y\), \(-z\), \(-x\)}, {y + 3/4, \(-z\), 
              x + 3/4}, {\(-y\), z + 3/4, x + 3/4}, {y + 3/4, 
              z + 3/4, \(-x\)}, {x, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/4, \(-y\) + 3/4, z + 1/2}, {\(-x\) + 1/4, 
              y + 1/2, \(-z\) + 3/4}, {x, \(-y\) + 3/4, \(-z\) + 3/4}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 3/4, \(-y\) + 3/4}, {\(-z\) + 
                1/4, \(-x\) + 3/4, y + 1/2}, {\(-z\) + 1/4, 
              x + 1/2, \(-y\) + 3/4}, {y, z + 1/2, x + 1/2}, {\(-y\) + 1/4, 
              z + 1/2, \(-x\) + 3/4}, {y, \(-z\) + 3/4, \(-x\) + 
                3/4}, {\(-y\) + 1/4, \(-z\) + 3/4, 
              x + 1/2}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x + 3/4, 
              y + 1/4, \(-z\) + 1/2}, {x + 3/4, \(-y\) + 1/2, 
              z + 1/4}, {\(-x\), y + 1/4, 
              z + 1/4}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x + 1/4, y + 1/4}, {z + 3/4, 
              x + 1/4, \(-y\) + 1/2}, {z + 3/4, \(-x\) + 1/2, 
              y + 1/4}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                3/4, \(-z\) + 1/2, x + 1/4}, {\(-y\), z + 1/4, 
              x + 1/4}, {y + 3/4, z + 1/4, \(-x\) + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 3/4, \(-y\) + 1/4, z + 1/2}, {\(-x\) + 3/4, 
              y, \(-z\) + 3/4}, {x + 1/2, \(-y\) + 1/4, \(-z\) + 3/4}, {z + 
                1/2, x, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/4, \(-y\) + 3/4}, {\(-z\) + 
                3/4, \(-x\) + 1/4, y + 1/2}, {\(-z\) + 3/4, 
              x, \(-y\) + 3/4}, {y + 1/2, z, x + 1/2}, {\(-y\) + 3/4, 
              z, \(-x\) + 3/4}, {y + 1/2, \(-z\) + 1/4, \(-x\) + 
                3/4}, {\(-y\) + 3/4, \(-z\) + 1/4, 
              x + 1/2}, {\(-x\) + 1/2, \(-y\), \(-z\) + 1/2}, {x + 1/4, 
              y + 3/4, \(-z\) + 1/2}, {x + 1/4, \(-y\), 
              z + 1/4}, {\(-x\) + 1/2, y + 3/4, 
              z + 1/4}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x + 3/4, y + 1/4}, {z + 1/4, 
              x + 3/4, \(-y\) + 1/2}, {z + 1/4, \(-x\), 
              y + 1/4}, {\(-y\) + 1/2, \(-z\), \(-x\) + 1/2}, {y + 
                1/4, \(-z\), x + 1/4}, {\(-y\) + 1/2, z + 3/4, 
              x + 1/4}, {y + 1/4, z + 3/4, \(-x\) + 1/2}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 3/4, \(-y\) + 3/4, z}, {\(-x\) + 3/4, 
              y + 1/2, \(-z\) + 1/4}, {x + 1/2, \(-y\) + 3/4, \(-z\) + 
                1/4}, {z + 1/2, x + 1/2, 
              y}, {z + 1/2, \(-x\) + 3/4, \(-y\) + 1/4}, {\(-z\) + 
                3/4, \(-x\) + 3/4, y}, {\(-z\) + 3/4, 
              x + 1/2, \(-y\) + 1/4}, {y + 1/2, z + 1/2, x}, {\(-y\) + 3/4, 
              z + 1/2, \(-x\) + 1/4}, {y + 1/2, \(-z\) + 3/4, \(-x\) + 
                1/4}, {\(-y\) + 3/4, \(-z\) + 3/4, 
              x}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/4, 
              y + 1/4, \(-z\)}, {x + 1/4, \(-y\) + 1/2, 
              z + 3/4}, {\(-x\) + 1/2, y + 1/4, 
              z + 3/4}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, 
              x + 1/4, y + 3/4}, {z + 1/4, 
              x + 1/4, \(-y\)}, {z + 1/4, \(-x\) + 1/2, 
              y + 3/4}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 
                1/4, \(-z\) + 1/2, x + 3/4}, {\(-y\) + 1/2, z + 1/4, 
              x + 3/4}, {y + 1/4, z + 1/4, \(-x\)}}, {"204 (Im-3)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), 
              x}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\) + 1/2, y + 1/2}, {\(-z\) + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, 
              x + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, x + 1/2, y + 1/2}, {z + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {z + 1/2, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                1/2, \(-z\) + 1/2, x + 1/2}, {\(-y\) + 1/2, z + 1/2, 
              x + 1/2}, {y + 1/2, 
              z + 1/2, \(-x\) + 1/2}}, {"205 (Pa-3)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), 
              x + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\) + 1/2, x + 1/2, 
              y}, {z + 1/2, x, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\) + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, z + 1/2, x}, {y + 1/2, 
              z, \(-x\) + 1/2}}, {"206 (Ia-3)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), 
              x + 1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\) + 1/2, x + 1/2, 
              y}, {z + 1/2, x, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\) + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, z + 1/2, x}, {y + 1/2, 
              z, \(-x\) + 1/2}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z, \(-x\), \(-y\) + 1/2}, {\(-z\), \(-x\) + 1/2, 
              y}, {\(-z\) + 1/2, x, \(-y\)}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\)}, {y, \(-z\), \(-x\) + 1/2}, {\(-y\), \(-z\) + 1/2, 
              x}, {\(-x\) + 1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z}, {\(-x\), y, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x, y + 1/2}, {z, x + 1/2, \(-y\)}, {z + 1/2, \(-x\), 
              y}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                1/2, \(-z\), x}, {\(-y\), z, x + 1/2}, {y, 
              z + 1/2, \(-x\)}}, {"207 (P432)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
              x}, {\(-z\), \(-y\), \(-x\)}}, {"208 (P4232)", {x, y, 
              z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/2, \(-z\) + 1/2, y + 1/2}, {z + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, y + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}}, {"209 (F432)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
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              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\) + 
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              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\)}, {y + 
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              x}, {\(-z\) + 1/2, y + 1/2, 
              x}, {\(-z\) + 1/2, \(-y\) + 
                1/2, \(-x\)}}, {"210 (F4132)", {x, y, 
              z}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
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              x}, {\(-y\) + 1/2, 
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              x + 1/2}, {\(-y\), 
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                3/4}, {y + 3/4, \(-x\) + 3/4, z + 1/4}, {\(-y\) + 1/4, 
              x + 3/4, z + 3/4}, {x + 1/4, 
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              y + 3/4}, {\(-x\) + 3/4, \(-z\) + 1/4, \(-y\) + 3/4}, {x + 
                3/4, \(-z\) + 3/4, y + 1/4}, {z + 1/4, 
              y + 1/4, \(-x\) + 1/4}, {z + 3/4, \(-y\) + 3/4, 
              x + 1/4}, {\(-z\) + 1/4, y + 3/4, 
              x + 3/4}, {\(-z\) + 3/4, \(-y\) + 1/4, \(-x\) + 3/4}, {x + 1/2, 
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              y}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x, \(-y\)}, {y + 1/2, z + 1/2, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\) + 1/2, \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), x + 1/2}, {y + 1/4, 
              x + 3/4, \(-z\) + 3/4}, {\(-y\) + 3/4, \(-x\) + 3/4, \(-z\) + 
                1/4}, {y + 3/4, \(-x\) + 1/4, z + 3/4}, {\(-y\) + 1/4, 
              x + 1/4, z + 1/4}, {x + 1/4, 
              z + 3/4, \(-y\) + 3/4}, {\(-x\) + 1/4, z + 1/4, 
              y + 1/4}, {\(-x\) + 3/4, \(-z\) + 3/4, \(-y\) + 1/4}, {x + 
                3/4, \(-z\) + 1/4, y + 3/4}, {z + 1/4, 
              y + 3/4, \(-x\) + 3/4}, {z + 3/4, \(-y\) + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, y + 1/4, 
              x + 1/4}, {\(-z\) + 3/4, \(-y\) + 3/4, \(-x\) + 
                1/4}}, {"211 (I432)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
              x}, {\(-z\), \(-y\), \(-x\)}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\) + 1/2, y + 1/2}, {\(-z\) + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, x + 1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/2, \(-z\) + 1/2, y + 1/2}, {z + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, y + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}}, {"212 (P4332)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
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              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {y + 1/4, 
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                1/4}, {y + 3/4, \(-x\) + 3/4, z + 1/4}, {\(-y\) + 3/4, 
              x + 1/4, z + 3/4}, {x + 1/4, 
              z + 3/4, \(-y\) + 3/4}, {\(-x\) + 3/4, z + 1/4, 
              y + 3/4}, {\(-x\) + 1/4, \(-z\) + 1/4, \(-y\) + 1/4}, {x + 
                3/4, \(-z\) + 3/4, y + 1/4}, {z + 1/4, 
              y + 3/4, \(-x\) + 3/4}, {z + 3/4, \(-y\) + 3/4, 
              x + 1/4}, {\(-z\) + 3/4, y + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, \(-y\) + 1/4, \(-x\) + 
                1/4}}, {"213 (P4132)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
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              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
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              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {y + 3/4, 
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                3/4}, {y + 1/4, \(-x\) + 1/4, z + 3/4}, {\(-y\) + 1/4, 
              x + 3/4, z + 1/4}, {x + 3/4, 
              z + 1/4, \(-y\) + 1/4}, {\(-x\) + 1/4, z + 3/4, 
              y + 1/4}, {\(-x\) + 3/4, \(-z\) + 3/4, \(-y\) + 3/4}, {x + 
                1/4, \(-z\) + 1/4, y + 3/4}, {z + 3/4, 
              y + 1/4, \(-x\) + 1/4}, {z + 1/4, \(-y\) + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, y + 3/4, 
              x + 1/4}, {\(-z\) + 3/4, \(-y\) + 3/4, \(-x\) + 
                3/4}}, {"214 (I4132)", {x, y, z}, {\(-x\) + 1/2, \(-y\), 
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              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
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              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {y + 3/4, 
              x + 1/4, \(-z\) + 1/4}, {\(-y\) + 3/4, \(-x\) + 3/4, \(-z\) + 
                3/4}, {y + 1/4, \(-x\) + 1/4, z + 3/4}, {\(-y\) + 1/4, 
              x + 3/4, z + 1/4}, {x + 3/4, 
              z + 1/4, \(-y\) + 1/4}, {\(-x\) + 1/4, z + 3/4, 
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                1/4, \(-z\) + 1/4, y + 3/4}, {z + 3/4, 
              y + 1/4, \(-x\) + 1/4}, {z + 1/4, \(-y\) + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, y + 3/4, 
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              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {z + 1/2, x + 1/2, 
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              y}, {\(-z\) + 1/2, x, \(-y\)}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\)}, {y, \(-z\), \(-x\) + 1/2}, {\(-y\), \(-z\) + 1/2, 
              x}, {y + 1/4, 
              x + 3/4, \(-z\) + 3/4}, {\(-y\) + 1/4, \(-x\) + 1/4, \(-z\) + 
                1/4}, {y + 3/4, \(-x\) + 3/4, z + 1/4}, {\(-y\) + 3/4, 
              x + 1/4, z + 3/4}, {x + 1/4, 
              z + 3/4, \(-y\) + 3/4}, {\(-x\) + 3/4, z + 1/4, 
              y + 3/4}, {\(-x\) + 1/4, \(-z\) + 1/4, \(-y\) + 1/4}, {x + 
                3/4, \(-z\) + 3/4, y + 1/4}, {z + 1/4, 
              y + 3/4, \(-x\) + 3/4}, {z + 3/4, \(-y\) + 3/4, 
              x + 1/4}, {\(-z\) + 3/4, y + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, \(-y\) + 1/4, \(-x\) + 
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              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
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              y}, {x, \(-z\), \(-y\)}, {z, y, 
              x}, {z, \(-y\), \(-x\)}, {\(-z\), y, \(-x\)}, {\(-z\), \(-y\), 
              x}}, {"216 (F-43m)", {x, y, z}, {\(-x\), \(-y\), 
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              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, x, 
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              y}, {x, \(-z\), \(-y\)}, {z, y, 
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              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
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              z + 1/2}, {y, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\), 
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              z + 1/2}, {\(-y\) + 1/2, \(-x\), 
              z + 1/2}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x, \(-z\) + 1/2}, {x + 1/2, z, y + 1/2}, {\(-x\) + 1/2, 
              z, \(-y\) + 1/2}, {\(-x\) + 1/2, \(-z\), 
              y + 1/2}, {x + 1/2, \(-z\), \(-y\) + 1/2}, {z + 1/2, y, 
              x + 1/2}, {z + 1/2, \(-y\), \(-x\) + 1/2}, {\(-z\) + 1/2, 
              y, \(-x\) + 1/2}, {\(-z\) + 1/2, \(-y\), x + 1/2}, {x + 1/2, 
              y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y + 1/2, x + 1/2, 
              z}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z}, {y + 1/2, \(-x\) + 1/2, \(-z\)}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\)}, {x + 1/2, z + 1/2, y}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\)}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y}, {x + 1/2, \(-z\) + 1/2, \(-y\)}, {z + 1/2, y + 1/2, 
              x}, {z + 1/2, \(-y\) + 1/2, \(-x\)}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\)}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x}}, {"217 (I-43m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, x, 
              z}, {\(-y\), \(-x\), z}, {y, \(-x\), \(-z\)}, {\(-y\), 
              x, \(-z\)}, {x, z, y}, {\(-x\), z, \(-y\)}, {\(-x\), \(-z\), 
              y}, {x, \(-z\), \(-y\)}, {z, y, 
              x}, {z, \(-y\), \(-x\)}, {\(-z\), y, \(-x\)}, {\(-z\), \(-y\), 
              x}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\) + 1/2, y + 1/2}, {\(-z\) + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, x + 1/2}, {y + 1/2, 
              x + 1/2, z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {z + 1/2, 
              y + 1/2, 
              x + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}}, {"218 (P-43n)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y + 1/2, 
              x + 1/2, z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {z + 1/2, 
              y + 1/2, 
              x + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}}, {"219 (F-43c)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y + 1/2, 
              x + 1/2, z + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {x + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {z + 1/2, 
              y + 1/2, 
              x + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {x, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), \(-x\) + 
                1/2, y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z + 1/2, 
              x + 1/2}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\), \(-z\) + 1/2, x + 1/2}, {y + 1/2, x, 
              z}, {\(-y\) + 1/2, \(-x\), 
              z}, {y + 1/2, \(-x\), \(-z\)}, {\(-y\) + 1/2, 
              x, \(-z\)}, {x + 1/2, z, y}, {\(-x\) + 1/2, 
              z, \(-y\)}, {\(-x\) + 1/2, \(-z\), 
              y}, {x + 1/2, \(-z\), \(-y\)}, {z + 1/2, y, 
              x}, {z + 1/2, \(-y\), \(-x\)}, {\(-z\) + 1/2, 
              y, \(-x\)}, {\(-z\) + 1/2, \(-y\), x}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}, {z + 1/2, x, 
              y + 1/2}, {z + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\), y + 1/2}, {\(-z\) + 1/2, 
              x, \(-y\) + 1/2}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y + 1/2, \(-z\), \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), x + 1/2}, {y, x + 1/2, 
              z}, {\(-y\), \(-x\) + 1/2, 
              z}, {y, \(-x\) + 1/2, \(-z\)}, {\(-y\), x + 1/2, \(-z\)}, {x, 
              z + 1/2, y}, {\(-x\), z + 1/2, \(-y\)}, {\(-x\), \(-z\) + 1/2, 
              y}, {x, \(-z\) + 1/2, \(-y\)}, {z, y + 1/2, 
              x}, {z, \(-y\) + 1/2, \(-x\)}, {\(-z\), 
              y + 1/2, \(-x\)}, {\(-z\), \(-y\) + 1/2, x}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y, x, z + 1/2}, {\(-y\), \(-x\), 
              z + 1/2}, {y, \(-x\), \(-z\) + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}, {x, z, y + 1/2}, {\(-x\), 
              z, \(-y\) + 1/2}, {\(-x\), \(-z\), 
              y + 1/2}, {x, \(-z\), \(-y\) + 1/2}, {z, y, 
              x + 1/2}, {z, \(-y\), \(-x\) + 1/2}, {\(-z\), 
              y, \(-x\) + 1/2}, {\(-z\), \(-y\), 
              x + 1/2}}, {"220 (I-43d)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {y + 1/4, 
              x + 1/4, z + 1/4}, {\(-y\) + 1/4, \(-x\) + 3/4, 
              z + 3/4}, {y + 3/4, \(-x\) + 1/4, \(-z\) + 3/4}, {\(-y\) + 3/4, 
              x + 3/4, \(-z\) + 1/4}, {x + 1/4, z + 1/4, 
              y + 1/4}, {\(-x\) + 3/4, 
              z + 3/4, \(-y\) + 1/4}, {\(-x\) + 1/4, \(-z\) + 3/4, 
              y + 3/4}, {x + 3/4, \(-z\) + 1/4, \(-y\) + 3/4}, {z + 1/4, 
              y + 1/4, 
              x + 1/4}, {z + 3/4, \(-y\) + 1/4, \(-x\) + 3/4}, {\(-z\) + 3/4, 
              y + 3/4, \(-x\) + 1/4}, {\(-z\) + 1/4, \(-y\) + 3/4, 
              x + 3/4}, {x + 1/2, y + 1/2, z + 1/2}, {\(-x\), \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z, \(-x\), \(-y\) + 1/2}, {\(-z\), \(-x\) + 1/2, 
              y}, {\(-z\) + 1/2, x, \(-y\)}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\)}, {y, \(-z\), \(-x\) + 1/2}, {\(-y\), \(-z\) + 1/2, 
              x}, {y + 3/4, x + 3/4, z + 3/4}, {\(-y\) + 3/4, \(-x\) + 1/4, 
              z + 1/4}, {y + 1/4, \(-x\) + 3/4, \(-z\) + 1/4}, {\(-y\) + 1/4, 
              x + 1/4, \(-z\) + 3/4}, {x + 3/4, z + 3/4, 
              y + 3/4}, {\(-x\) + 1/4, 
              z + 1/4, \(-y\) + 3/4}, {\(-x\) + 3/4, \(-z\) + 1/4, 
              y + 1/4}, {x + 1/4, \(-z\) + 3/4, \(-y\) + 1/4}, {z + 3/4, 
              y + 3/4, 
              x + 3/4}, {z + 1/4, \(-y\) + 3/4, \(-x\) + 1/4}, {\(-z\) + 1/4, 
              y + 1/4, \(-x\) + 3/4}, {\(-z\) + 3/4, \(-y\) + 1/4, 
              x + 1/4}}, {"221 (Pm-3m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
              x}, {\(-z\), \(-y\), \(-x\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, y}, {z, 
              x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {\(-y\), \(-x\), z}, {y, x, z}, {\(-y\), 
              x, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-x\), \(-z\), 
              y}, {x, \(-z\), \(-y\)}, {x, z, y}, {\(-x\), 
              z, \(-y\)}, {\(-z\), \(-y\), x}, {\(-z\), 
              y, \(-x\)}, {z, \(-y\), \(-x\)}, {z, y, 
              x}}, {"222 (Pn-3n)", {x, y, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, x, 
              y}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x, \(-y\) + 1/2}, {y, z, 
              x}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y, 
              x, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y, \(-x\) + 1/2, z}, {\(-y\) + 1/2, x, z}, {x, 
              z, \(-y\) + 1/2}, {\(-x\) + 1/2, z, 
              y}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x, \(-z\) + 
                1/2, y}, {z, y, \(-x\) + 1/2}, {z, \(-y\) + 1/2, 
              x}, {\(-z\) + 1/2, y, 
              x}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x + 1/2, 
              y + 1/2}, {z + 1/2, x + 1/2, \(-y\)}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y + 1/2, \(-z\), 
              x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y + 1/2, 
              z + 1/2, \(-x\)}, {\(-y\), \(-x\), z + 1/2}, {y + 1/2, x + 1/2, 
              z + 1/2}, {\(-y\), 
              x + 1/2, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-x\), \(-z\), 
              y + 1/2}, {x + 1/2, \(-z\), \(-y\)}, {x + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\), z + 1/2, \(-y\)}, {\(-z\), \(-y\), 
              x + 1/2}, {\(-z\), 
              y + 1/2, \(-x\)}, {z + 1/2, \(-y\), \(-x\)}, {z + 1/2, y + 1/2, 
              x + 1/2}}, {"223 (Pm-3n)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/2, \(-z\) + 1/2, y + 1/2}, {z + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, y + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, x + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 1/2, 
              z + 1/2, y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {z + 1/2, y + 1/2, x + 1/2}}, {"224 (Pn-3m)", {x, 
              y, z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, x, 
              y}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x, \(-y\) + 1/2}, {y, z, 
              x}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y + 1/2, \(-x\), 
              z + 1/2}, {\(-y\), x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\)}, {\(-x\), z + 1/2, 
              y + 1/2}, {\(-x\), \(-z\), \(-y\)}, {x + 1/2, \(-z\), 
              y + 1/2}, {z + 1/2, y + 1/2, \(-x\)}, {z + 1/2, \(-y\), 
              x + 1/2}, {\(-z\), y + 1/2, 
              x + 1/2}, {\(-z\), \(-y\), \(-x\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\), y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x + 1/2, 
              y + 1/2}, {z + 1/2, x + 1/2, \(-y\)}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y + 1/2, \(-z\), 
              x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y + 1/2, 
              z + 1/2, \(-x\)}, {\(-y\) + 1/2, \(-x\) + 1/2, z}, {y, x, 
              z}, {\(-y\) + 1/2, 
              x, \(-z\) + 1/2}, {y, \(-x\) + 1/2, \(-z\) + 1/2}, {\(-x\) + 
                1/2, \(-z\) + 1/2, y}, {x, \(-z\) + 1/2, \(-y\) + 1/2}, {x, 
              z, y}, {\(-x\) + 1/2, 
              z, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x}, {\(-z\) + 1/2, 
              y, \(-x\) + 1/2}, {z, \(-y\) + 1/2, \(-x\) + 1/2}, {z, y, 
              x}}, {"225 (Fm-3m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
              x}, {\(-z\), \(-y\), \(-x\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, y}, {z, 
              x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {\(-y\), \(-x\), z}, {y, x, z}, {\(-y\), 
              x, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-x\), \(-z\), 
              y}, {x, \(-z\), \(-y\)}, {x, z, y}, {\(-x\), 
              z, \(-y\)}, {\(-z\), \(-y\), x}, {\(-z\), 
              y, \(-x\)}, {z, \(-y\), \(-x\)}, {z, y, x}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), \(-x\) + 
                1/2, y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z + 1/2, 
              x + 1/2}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\), \(-z\) + 1/2, x + 1/2}, {y, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\), \(-x\) + 1/2, \(-z\) + 
                1/2}, {y, \(-x\) + 1/2, z + 1/2}, {\(-y\), x + 1/2, 
              z + 1/2}, {x, z + 1/2, \(-y\) + 1/2}, {\(-x\), z + 1/2, 
              y + 1/2}, {\(-x\), \(-z\) + 1/2, \(-y\) + 1/2}, {x, \(-z\) + 
                1/2, y + 1/2}, {z, y + 1/2, \(-x\) + 1/2}, {z, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\), y + 1/2, 
              x + 1/2}, {\(-z\), \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x + 1/2, y + 1/2}, {z, 
              x + 1/2, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 
                1/2, x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y, 
              z + 1/2, \(-x\) + 1/2}, {\(-y\), \(-x\) + 1/2, z + 1/2}, {y, 
              x + 1/2, z + 1/2}, {\(-y\), 
              x + 1/2, \(-z\) + 1/2}, {y, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\), \(-z\) + 1/2, 
              y + 1/2}, {x, \(-z\) + 1/2, \(-y\) + 1/2}, {x, z + 1/2, 
              y + 1/2}, {\(-x\), 
              z + 1/2, \(-y\) + 1/2}, {\(-z\), \(-y\) + 1/2, 
              x + 1/2}, {\(-z\), 
              y + 1/2, \(-x\) + 1/2}, {z, \(-y\) + 1/2, \(-x\) + 1/2}, {z, 
              y + 1/2, x + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}\ 1, {z + 1/2, 
              x, y + 1/2}, {z + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\), y + 1/2}, {\(-z\) + 1/2, 
              x, \(-y\) + 1/2}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y + 1/2, \(-z\), \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), x + 1/2}, {y + 1/2, 
              x, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\), \(-z\) + 1/2}\ 1, {y + 
                1/2, \(-x\), z + 1/2}, {\(-y\) + 1/2, x, z + 1/2}, {x + 1/2, 
              z, \(-y\) + 1/2}, {\(-x\) + 1/2, z, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\), \(-y\) + 1/2}, {x + 
                1/2, \(-z\), y + 1/2}, {z + 1/2, 
              y, \(-x\) + 1/2}, {z + 1/2, \(-y\), x + 1/2}, {\(-z\) + 1/2, y, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\), \(-x\) + 1/2}\ 1, {\(-x\) + 
                1/2, \(-y\), \(-z\) + 1/2}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x, y + 1/2}, {z + 1/2, x, \(-y\) + 1/2}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\) + 1/2, \(-z\), \(-x\) + 
                1/2}, {y + 1/2, \(-z\), x + 1/2}\ 1, {\(-y\) + 1/2, z, 
              x + 1/2}, {y + 1/2, z, \(-x\) + 1/2}, {\(-y\) + 1/2, \(-x\), 
              z + 1/2}, {y + 1/2, x, z + 1/2}, {\(-y\) + 1/2, 
              x, \(-z\) + 1/2}, {y + 1/2, \(-x\), \(-z\) + 1/2}, {\(-x\) + 
                1/2, \(-z\), 
              y + 1/2}, {x + 1/2, \(-z\), \(-y\) + 1/2}, {x + 1/2, z, 
              y + 1/2}, {\(-x\) + 1/2, z, \(-y\) + 1/2}\ 1, {\(-z\) + 
                1/2, \(-y\), x + 1/2}, {\(-z\) + 1/2, 
              y, \(-x\) + 1/2}, {z + 1/2, \(-y\), \(-x\) + 1/2}, {z + 1/2, y, 
              x + 1/2}, {x + 1/2, y + 1/2, z}, {\(-x\) + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}\ 1, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y + 1/2, 
              x + 1/2, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\)}, {y + 
                1/2, \(-x\) + 1/2, 
              z}, {\(-y\) + 1/2, x + 1/2, z}\ 1, {x + 1/2, 
              z + 1/2, \(-y\)}, {\(-x\) + 1/2, z + 1/2, 
              y}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\)}, {x + 1/2, \(-z\) + 
                1/2, y}, {z + 1/2, y + 1/2, \(-x\)}, {z + 1/2, \(-y\) + 1/2, 
              x}, {\(-z\) + 1/2, y + 1/2, 
              x}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
                y + 1/2, \(-z\)}\ 1, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, 
              x + 1/2, y}, {z + 1/2, 
              x + 1/2, \(-y\)}, {z + 1/2, \(-x\) + 1/2, 
              y}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 
                1/2, x}, {\(-y\) + 1/2, z + 1/2, 
              x}, {y + 1/2, z + 1/2, \(-x\)}\ 1, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z}, {y + 1/2, x + 1/2, z}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\)}, {y + 1/2, \(-x\) + 1/2, \(-z\)}, {\(-x\) + 
                1/2, \(-z\) + 1/2, 
              y}, {x + 1/2, \(-z\) + 1/2, \(-y\)}, {x + 1/2, z + 1/2, 
              y}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x}, {\(-z\) + 1/2, y + 1/2, \(-x\)}\ 1, {z + 1/2, \(-y\) + 
                1/2, \(-x\)}, {z + 1/2, y + 1/2, x}}, {"226 (Fm-3c)", {x, 
              y, z}, {\(-x\), \(-y\), z}, {\(-x\), 
              y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/2, \(-z\) + 1/2, y + 1/2}, {z + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, y + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x, y, \(-z\)}, {x, \(-y\), 
              z}, {\(-x\), y, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, 
              y}, {z, x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, x + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 1/2, 
              z + 1/2, y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {z + 1/2, y + 1/2, x + 1/2}, {x, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, \(-z\) + 1/2}, {z, 
              x + 1/2, 
              y + 1/2}, {z, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), \(-x\) + 
                1/2, y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z + 1/2, 
              x + 1/2}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\), \(-z\) + 1/2, x + 1/2}, {y + 1/2, 
              x, \(-z\)}, {\(-y\) + 1/2, \(-x\), \(-z\)}, {y + 1/2, \(-x\), 
              z}, {\(-y\) + 1/2, x, z}, {x + 1/2, z, \(-y\)}, {\(-x\) + 1/2, 
              z, y}, {\(-x\) + 1/2, \(-z\), \(-y\)}, {x + 1/2, \(-z\), 
              y}, {z + 1/2, y, \(-x\)}, {z + 1/2, \(-y\), x}, {\(-z\) + 1/2, 
              y, x}, {\(-z\) + 1/2, \(-y\), \(-x\)}, {\(-x\), \(-y\) + 
                1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\), 
              y + 1/2, 
              z + 1/2}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x + 1/2, y + 1/2}, {z, 
              x + 1/2, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y, \(-z\) + 
                1/2, x + 1/2}, {\(-y\), z + 1/2, x + 1/2}, {y, 
              z + 1/2, \(-x\) + 1/2}, {\(-y\) + 1/2, \(-x\), z}, {y + 1/2, x, 
              z}, {\(-y\) + 1/2, 
              x, \(-z\)}, {y + 1/2, \(-x\), \(-z\)}, {\(-x\) + 1/2, \(-z\), 
              y}, {x + 1/2, \(-z\), \(-y\)}, {x + 1/2, z, y}, {\(-x\) + 1/2, 
              z, \(-y\)}, {\(-z\) + 1/2, \(-y\), x}, {\(-z\) + 1/2, 
              y, \(-x\)}, {z + 1/2, \(-y\), \(-x\)}, {z + 1/2, y, 
              x}, {x + 1/2, y, z + 1/2}, {\(-x\) + 1/2, \(-y\), 
              z + 1/2}, {\(-x\) + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), \(-z\) + 1/2}\ 1, {z + 1/2, 
              x, y + 1/2}, {z + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\), y + 1/2}, {\(-z\) + 1/2, 
              x, \(-y\) + 1/2}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\) + 1/2}, {y + 1/2, \(-z\), \(-x\) + 1/2}, {\(-y\) + 
                1/2, \(-z\), x + 1/2}, {y, 
              x + 1/2, \(-z\)}, {\(-y\), \(-x\) + 
                  1/2, \(-z\)}\ 1, {y, \(-x\) + 1/2, z}, {\(-y\), x + 1/2, 
              z}, {x, z + 1/2, \(-y\)}, {\(-x\), z + 1/2, 
              y}, {\(-x\), \(-z\) + 1/2, \(-y\)}, {x, \(-z\) + 1/2, y}, {z, 
              y + 1/2, \(-x\)}, {z, \(-y\) + 1/2, x}, {\(-z\), y + 1/2, 
              x}, {\(-z\), \(-y\) + 1/2, \(-x\)}\ 1, {\(-x\) + 
                1/2, \(-y\), \(-z\) + 1/2}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x + 1/2, \(-y\), z + 1/2}, {\(-x\) + 1/2, y, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x, y + 1/2}, {z + 1/2, x, \(-y\) + 1/2}, {z + 1/2, \(-x\), 
              y + 1/2}, {\(-y\) + 1/2, \(-z\), \(-x\) + 
                1/2}, {y + 1/2, \(-z\), x + 1/2}\ 1, {\(-y\) + 1/2, z, 
              x + 1/2}, {y + 1/2, z, \(-x\) + 1/2}, {\(-y\), \(-x\) + 1/2, 
              z}, {y, x + 1/2, z}, {\(-y\), 
              x + 1/2, \(-z\)}, {y, \(-x\) + 1/2, \(-z\)}, {\(-x\), \(-z\) + 
                1/2, y}, {x, \(-z\) + 1/2, \(-y\)}, {x, z + 1/2, 
              y}, {\(-x\), z + 1/2, \(-y\)}\ 1, {\(-z\), \(-y\) + 1/2, 
              x}, {\(-z\), y + 1/2, \(-x\)}, {z, \(-y\) + 1/2, \(-x\)}, {z, 
              y + 1/2, x}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/2, \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z + 1/2, 
              x + 1/2, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}\ 1, {\(-z\) + 1/2, \(-x\) + 
                1/2, y}, {\(-z\) + 1/2, x + 1/2, \(-y\)}, {y + 1/2, z + 1/2, 
              x}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 1/2, \(-x\)}, {\(-y\) + 
                1/2, \(-z\) + 1/2, x}, {y, 
              x, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\) + 1/2}, {y, \(-x\), 
              z + 1/2}, {\(-y\), x, z + 1/2}\ 1, {x, 
              z, \(-y\) + 1/2}, {\(-x\), z, 
              y + 1/2}, {\(-x\), \(-z\), \(-y\) + 1/2}, {x, \(-z\), 
              y + 1/2}, {z, y, \(-x\) + 1/2}, {z, \(-y\), x + 1/2}, {\(-z\), 
              y, x + 1/2}, {\(-z\), \(-y\), \(-x\) + 1/2}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/2, 
                y + 1/2, \(-z\)}\ 1, {x + 1/2, \(-y\) + 1/2, 
              z}, {\(-x\) + 1/2, y + 1/2, 
              z}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, 
              x + 1/2, y}, {z + 1/2, 
              x + 1/2, \(-y\)}, {z + 1/2, \(-x\) + 1/2, 
              y}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 1/2, \(-z\) + 
                1/2, x}, {\(-y\) + 1/2, z + 1/2, 
              x}, {y + 1/2, z + 1/2, \(-x\)}\ 1, {\(-y\), \(-x\), 
              z + 1/2}, {y, x, z + 1/2}, {\(-y\), 
              x, \(-z\) + 1/2}, {y, \(-x\), \(-z\) + 1/2}, {\(-x\), \(-z\), 
              y + 1/2}, {x, \(-z\), \(-y\) + 1/2}, {x, z, y + 1/2}, {\(-x\), 
              z, \(-y\) + 1/2}, {\(-z\), \(-y\), 
              x + 1/2}, {\(-z\), y, \(-x\) + 1/2}\ 1, {z, \(-y\), \(-x\) + 
                1/2}, {z, y, x + 1/2}}, {"227 (Fd-3m)", {x, y, 
              z}, {\(-x\) + 3/4, \(-y\) + 1/4, z + 1/2}, {\(-x\) + 1/4, 
              y + 1/2, \(-z\) + 3/4}, {x + 1/2, \(-y\) + 3/4, \(-z\) + 
                1/4}, {z, x, 
              y}, {z + 1/2, \(-x\) + 3/4, \(-y\) + 1/4}, {\(-z\) + 
                3/4, \(-x\) + 1/4, y + 1/2}, {\(-z\) + 1/4, 
              x + 1/2, \(-y\) + 3/4}, {y, z, x}, {\(-y\) + 1/4, 
              z + 1/2, \(-x\) + 3/4}, {y + 1/2, \(-z\) + 3/4, \(-x\) + 
                1/4}, {\(-y\) + 3/4, \(-z\) + 1/4, x + 1/2}, {y + 3/4, 
              x + 1/4, \(-z\) + 1/2}, {\(-y\), \(-x\), \(-z\)}, {y + 
                1/4, \(-x\) + 1/2, z + 3/4}, {\(-y\) + 1/2, x + 3/4, 
              z + 1/4}, {x + 3/4, z + 1/4, \(-y\) + 1/2}, {\(-x\) + 1/2, 
              z + 3/4, 
              y + 1/4}, {\(-x\), \(-z\), \(-y\)}, {x + 1/4, \(-z\) + 1/2, 
              y + 3/4}, {z + 3/4, 
              y + 1/4, \(-x\) + 1/2}, {z + 1/4, \(-y\) + 1/2, 
              x + 3/4}, {\(-z\) + 1/2, y + 3/4, 
              x + 1/4}, {\(-z\), \(-y\), \(-x\)}, {\(-x\), \(-y\), \(-z\)}, {x + 1/4, y + 3/4, \(-z\) + 1/2}, {x + 3/4, \(-y\) + 1/2, 
              z + 1/4}, {\(-x\) + 1/2, y + 1/4, 
              z + 3/4}, {\(-z\), \(-x\), \(-y\)}, {\(-z\) + 1/2, x + 1/4, 
              y + 3/4}, {z + 1/4, 
              x + 3/4, \(-y\) + 1/2}, {z + 3/4, \(-x\) + 1/2, 
              y + 1/4}, {\(-y\), \(-z\), \(-x\)}, {y + 3/4, \(-z\) + 1/2, 
              x + 1/4}, {\(-y\) + 1/2, z + 1/4, x + 3/4}, {y + 1/4, 
              z + 3/4, \(-x\) + 1/2}, {\(-y\) + 1/4, \(-x\) + 3/4, 
              z + 1/2}, {y, x, z}, {\(-y\) + 3/4, 
              x + 1/2, \(-z\) + 1/4}, {y + 1/2, \(-x\) + 1/4, \(-z\) + 
                3/4}, {\(-x\) + 1/4, \(-z\) + 3/4, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/4, \(-y\) + 3/4}, {x, z, 
              y}, {\(-x\) + 3/4, 
              z + 1/2, \(-y\) + 1/4}, {\(-z\) + 1/4, \(-y\) + 3/4, 
              x + 1/2}, {\(-z\) + 3/4, 
              y + 1/2, \(-x\) + 1/4}, {z + 1/2, \(-y\) + 1/4, \(-x\) + 
                3/4}, {z, y, x}, {x, y + 1/2, 
              z + 1/2}, {\(-x\) + 3/4, \(-y\) + 3/4, z}, {\(-x\) + 1/4, 
              y, \(-z\) + 1/4}, {x + 1/2, \(-y\) + 1/4, \(-z\) + 3/4}, {z, 
              x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/4, \(-y\) + 3/4}, {\(-z\) + 
                3/4, \(-x\) + 3/4, y}, {\(-z\) + 1/4, x, \(-y\) + 1/4}, {y, 
              z + 1/2, x + 1/2}, {\(-y\) + 1/4, 
              z, \(-x\) + 1/4}, {y + 1/2, \(-z\) + 1/4, \(-x\) + 
                3/4}, {\(-y\) + 3/4, \(-z\) + 3/4, x}, {y + 3/4, 
              x + 3/4, \(-z\)}, {\(-y\), \(-x\) + 1/2, \(-z\) + 1/2}, {y + 
                1/4, \(-x\), z + 1/4}, {\(-y\) + 1/2, x + 1/4, 
              z + 3/4}, {x + 3/4, z + 3/4, \(-y\)}, {\(-x\) + 1/2, z + 1/4, 
              y + 3/4}, {\(-x\), \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/4, \(-z\), y + 1/4}, {z + 3/4, 
              y + 3/4, \(-x\)}, {z + 1/4, \(-y\), x + 1/4}, {\(-z\) + 1/2, 
              y + 1/4, 
              x + 3/4}, {\(-z\), \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/4, 
              y + 1/4, \(-z\)}, {x + 3/4, \(-y\), z + 3/4}, {\(-x\) + 1/2, 
              y + 3/4, 
              z + 1/4}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x + 3/4, y + 1/4}, {z + 1/4, 
              x + 1/4, \(-y\)}, {z + 3/4, \(-x\), 
              y + 3/4}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                3/4, \(-z\), x + 3/4}, {\(-y\) + 1/2, z + 3/4, 
              x + 1/4}, {y + 1/4, 
              z + 1/4, \(-x\)}, {\(-y\) + 1/4, \(-x\) + 1/4, z}, {y, x + 1/2, 
              z + 1/2}, {\(-y\) + 3/4, 
              x, \(-z\) + 3/4}, {y + 1/2, \(-x\) + 3/4, \(-z\) + 
                1/4}, {\(-x\) + 1/4, \(-z\) + 1/4, 
              y}, {x + 1/2, \(-z\) + 3/4, \(-y\) + 1/4}, {x, z + 1/2, 
              y + 1/2}, {\(-x\) + 3/4, 
              z, \(-y\) + 3/4}, {\(-z\) + 1/4, \(-y\) + 1/4, 
              x}, {\(-z\) + 3/4, 
              y, \(-x\) + 3/4}, {z + 1/2, \(-y\) + 3/4, \(-x\) + 1/4}, {z, 
              y + 1/2, x + 1/2}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 1/4, \(-y\) + 1/4, z}, {\(-x\) + 3/4, 
              y + 1/2, \(-z\) + 
                1/4}, {x, \(-y\) + 3/4, \(-z\) + 3/4}\ 1, {z + 1/2, x, 
              y + 1/2}, {z, \(-x\) + 3/4, \(-y\) + 3/4}, {\(-z\) + 
                1/4, \(-x\) + 1/4, y}, {\(-z\) + 3/4, 
              x + 1/2, \(-y\) + 1/4}, {y + 1/2, z, x + 1/2}, {\(-y\) + 3/4, 
              z + 1/2, \(-x\) + 1/4}, {y, \(-z\) + 3/4, \(-x\) + 
                3/4}, {\(-y\) + 1/4, \(-z\) + 1/4, x}, {y + 1/4, 
              x + 1/4, \(-z\)}, {\(-y\) + 1/2, \(-x\), \(-z\) + 1/2}\ 1, {y + 
                3/4, \(-x\) + 1/2, z + 1/4}, {\(-y\), x + 3/4, 
              z + 3/4}, {x + 1/4, z + 1/4, \(-y\)}, {\(-x\), z + 3/4, 
              y + 3/4}, {\(-x\) + 1/2, \(-z\), \(-y\) + 1/2}, {x + 
                3/4, \(-z\) + 1/2, y + 1/4}, {z + 1/4, 
              y + 1/4, \(-x\)}, {z + 3/4, \(-y\) + 1/2, x + 1/4}, {\(-z\), 
              y + 3/4, 
              x + 3/4}, {\(-z\) + 1/2, \(-y\), \(-x\) + 1/2}\ 1, {\(-x\) + 
                1/2, \(-y\), \(-z\) + 1/2}, {x + 3/4, 
              y + 3/4, \(-z\)}, {x + 1/4, \(-y\) + 1/2, z + 3/4}, {\(-x\), 
              y + 1/4, 
              z + 1/4}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\), 
              x + 1/4, y + 1/4}, {z + 3/4, 
              x + 3/4, \(-y\)}, {z + 1/4, \(-x\) + 1/2, 
              y + 3/4}, {\(-y\) + 1/2, \(-z\), \(-x\) + 
                1/2}, {y + 1/4, \(-z\) + 1/2, x + 3/4}\ 1, {\(-y\), z + 1/4, 
              x + 1/4}, {y + 3/4, 
              z + 3/4, \(-x\)}, {\(-y\) + 3/4, \(-x\) + 3/4, z}, {y + 1/2, x, 
              z + 1/2}, {\(-y\) + 1/4, 
              x + 1/2, \(-z\) + 3/4}, {y, \(-x\) + 1/4, \(-z\) + 
                1/4}, {\(-x\) + 3/4, \(-z\) + 3/4, 
              y}, {x, \(-z\) + 1/4, \(-y\) + 1/4}, {x + 1/2, z, 
              y + 1/2}, {\(-x\) + 1/4, z + 1/2, \(-y\) + 3/4}\ 1, {\(-z\) + 
                3/4, \(-y\) + 3/4, x}, {\(-z\) + 1/4, 
              y + 1/2, \(-x\) + 3/4}, {z, \(-y\) + 1/4, \(-x\) + 1/4}, {z + 
                1/2, y, x + 1/2}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 1/4, \(-y\) + 3/4, z + 1/2}, {\(-x\) + 3/4, 
              y, \(-z\) + 3/4}, {x, \(-y\) + 1/4, \(-z\) + 1/4}, {z + 1/2, 
              x + 1/2, 
              y}, {z, \(-x\) + 1/4, \(-y\) + 1/4}\ 1, {\(-z\) + 1/4, \(-x\) + 
                3/4, y + 1/2}, {\(-z\) + 3/4, x, \(-y\) + 3/4}, {y + 1/2, 
              z + 1/2, x}, {\(-y\) + 3/4, 
              z, \(-x\) + 3/4}, {y, \(-z\) + 1/4, \(-x\) + 1/4}, {\(-y\) + 
                1/4, \(-z\) + 3/4, x + 1/2}, {y + 1/4, 
              x + 3/4, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 
                1/2, \(-z\)}, {y + 3/4, \(-x\), 
              z + 3/4}, {\(-y\), x + 1/4, z + 1/4}\ 1, {x + 1/4, 
              z + 3/4, \(-y\) + 1/2}, {\(-x\), z + 1/4, 
              y + 1/4}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\)}, {x + 
                3/4, \(-z\), y + 3/4}, {z + 1/4, 
              y + 3/4, \(-x\) + 1/2}, {z + 3/4, \(-y\), x + 3/4}, {\(-z\), 
              y + 1/4, 
              x + 1/4}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\)}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 3/4, 
                y + 1/4, \(-z\) + 1/2}\ 1, {x + 1/4, \(-y\), 
              z + 1/4}, {\(-x\), y + 3/4, 
              z + 3/4}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\), 
              x + 3/4, y + 3/4}, {z + 3/4, 
              x + 1/4, \(-y\) + 1/2}, {z + 1/4, \(-x\), 
              y + 1/4}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 
                1/4, \(-z\), x + 1/4}, {\(-y\), z + 3/4, 
              x + 3/4}, {y + 3/4, z + 1/4, \(-x\) + 1/2}\ 1, {\(-y\) + 
                3/4, \(-x\) + 1/4, z + 1/2}, {y + 1/2, x + 1/2, 
              z}, {\(-y\) + 1/4, 
              x, \(-z\) + 1/4}, {y, \(-x\) + 3/4, \(-z\) + 3/4}, {\(-x\) + 
                3/4, \(-z\) + 1/4, 
              y + 1/2}, {x, \(-z\) + 3/4, \(-y\) + 3/4}, {x + 1/2, z + 1/2, 
              y}, {\(-x\) + 1/4, 
              z, \(-y\) + 1/4}, {\(-z\) + 3/4, \(-y\) + 1/4, 
              x + 1/2}, {\(-z\) + 1/4, y, \(-x\) + 1/4}\ 1, {z, \(-y\) + 
                3/4, \(-x\) + 3/4}, {z + 1/2, y + 1/2, 
              x}}, {"228 (Fd-3c)", {x, y, 
              z}, {\(-x\) + 1/4, \(-y\) + 3/4, z + 1/2}, {\(-x\) + 3/4, 
              y + 1/2, \(-z\) + 1/4}, {x + 1/2, \(-y\) + 1/4, \(-z\) + 
                3/4}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/4, \(-y\) + 3/4}, {\(-z\) + 
                1/4, \(-x\) + 3/4, y + 1/2}, {\(-z\) + 3/4, 
              x + 1/2, \(-y\) + 1/4}, {y, z, x}, {\(-y\) + 3/4, 
              z + 1/2, \(-x\) + 1/4}, {y + 1/2, \(-z\) + 1/4, \(-x\) + 
                3/4}, {\(-y\) + 1/4, \(-z\) + 3/4, x + 1/2}, {y + 3/4, 
              x + 1/4, \(-z\)}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/4, \(-x\), z + 3/4}, {\(-y\), x + 3/4, 
              z + 1/4}, {x + 3/4, z + 1/4, \(-y\)}, {\(-x\), z + 3/4, 
              y + 1/4}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/4, \(-z\), y + 3/4}, {z + 3/4, 
              y + 1/4, \(-x\)}, {z + 1/4, \(-y\), x + 3/4}, {\(-z\), y + 3/4, 
              x + 1/4}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {\(-x\), \(-y\), \(-z\)}, {x + 3/4, 
              y + 1/4, \(-z\) + 1/2}, {x + 1/4, \(-y\) + 1/2, 
              z + 3/4}, {\(-x\) + 1/2, y + 3/4, 
              z + 1/4}, {\(-z\), \(-x\), \(-y\)}, {\(-z\) + 1/2, x + 3/4, 
              y + 1/4}, {z + 3/4, 
              x + 1/4, \(-y\) + 1/2}, {z + 1/4, \(-x\) + 1/2, 
              y + 3/4}, {\(-y\), \(-z\), \(-x\)}, {y + 1/4, \(-z\) + 1/2, 
              x + 3/4}, {\(-y\) + 1/2, z + 3/4, x + 1/4}, {y + 3/4, 
              z + 1/4, \(-x\) + 1/2}, {\(-y\) + 1/4, \(-x\) + 3/4, 
              z}, {y + 1/2, x + 1/2, z + 1/2}, {\(-y\) + 3/4, 
              x, \(-z\) + 1/4}, {y, \(-x\) + 1/4, \(-z\) + 3/4}, {\(-x\) + 
                1/4, \(-z\) + 3/4, 
              y}, {x, \(-z\) + 1/4, \(-y\) + 3/4}, {x + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 3/4, 
              z, \(-y\) + 1/4}, {\(-z\) + 1/4, \(-y\) + 3/4, 
              x}, {\(-z\) + 3/4, 
              y, \(-x\) + 1/4}, {z, \(-y\) + 1/4, \(-x\) + 3/4}, {z + 1/2, 
              y + 1/2, x + 1/2}, {x, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/4, \(-y\) + 1/4, z}, {\(-x\) + 3/4, 
              y, \(-z\) + 3/4}, {x + 1/2, \(-y\) + 3/4, \(-z\) + 1/4}, {z, 
              x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 3/4, \(-y\) + 1/4}, {\(-z\) + 
                1/4, \(-x\) + 1/4, y}, {\(-z\) + 3/4, x, \(-y\) + 3/4}, {y, 
              z + 1/2, x + 1/2}, {\(-y\) + 3/4, 
              z, \(-x\) + 3/4}, {y + 1/2, \(-z\) + 3/4, \(-x\) + 
                1/4}, {\(-y\) + 1/4, \(-z\) + 1/4, x}, {y + 3/4, 
              x + 3/4, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\), \(-z\)}, {y + 
                1/4, \(-x\) + 1/2, z + 1/4}, {\(-y\), x + 1/4, 
              z + 3/4}, {x + 3/4, z + 3/4, \(-y\) + 1/2}, {\(-x\), z + 1/4, 
              y + 3/4}, {\(-x\) + 1/2, \(-z\), \(-y\)}, {x + 1/4, \(-z\) + 
                1/2, y + 1/4}, {z + 3/4, 
              y + 3/4, \(-x\) + 1/2}, {z + 1/4, \(-y\) + 1/2, 
              x + 1/4}, {\(-z\), y + 1/4, 
              x + 3/4}, {\(-z\) + 1/2, \(-y\), \(-x\)}, {\(-x\), \(-y\) + 
                1/2, \(-z\) + 1/2}, {x + 3/4, 
              y + 3/4, \(-z\)}, {x + 1/4, \(-y\), z + 1/4}, {\(-x\) + 1/2, 
              y + 1/4, 
              z + 3/4}, {\(-z\), \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, 
              x + 1/4, y + 3/4}, {z + 3/4, 
              x + 3/4, \(-y\)}, {z + 1/4, \(-x\), 
              y + 1/4}, {\(-y\), \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                1/4, \(-z\), x + 1/4}, {\(-y\) + 1/2, z + 1/4, 
              x + 3/4}, {y + 3/4, 
              z + 3/4, \(-x\)}, {\(-y\) + 1/4, \(-x\) + 1/4, 
              z + 1/2}, {y + 1/2, x, z}, {\(-y\) + 3/4, 
              x + 1/2, \(-z\) + 3/4}, {y, \(-x\) + 3/4, \(-z\) + 
                1/4}, {\(-x\) + 1/4, \(-z\) + 1/4, 
              y + 1/2}, {x, \(-z\) + 3/4, \(-y\) + 1/4}, {x + 1/2, z, 
              y}, {\(-x\) + 3/4, 
              z + 1/2, \(-y\) + 3/4}, {\(-z\) + 1/4, \(-y\) + 1/4, 
              x + 1/2}, {\(-z\) + 3/4, 
              y + 1/2, \(-x\) + 3/4}, {z, \(-y\) + 3/4, \(-x\) + 1/4}, {z + 
                1/2, y, x}, {x + 1/2, y, 
              z + 1/2}, {\(-x\) + 3/4, \(-y\) + 3/4, z}, {\(-x\) + 1/4, 
              y + 1/2, \(-z\) + 
                3/4}, {x, \(-y\) + 1/4, \(-z\) + 1/4}\ 1, {z + 1/2, x, 
              y + 1/2}, {z, \(-x\) + 1/4, \(-y\) + 1/4}, {\(-z\) + 
                3/4, \(-x\) + 3/4, y}, {\(-z\) + 1/4, 
              x + 1/2, \(-y\) + 3/4}, {y + 1/2, z, x + 1/2}, {\(-y\) + 1/4, 
              z + 1/2, \(-x\) + 3/4}, {y, \(-z\) + 1/4, \(-x\) + 
                1/4}, {\(-y\) + 3/4, \(-z\) + 3/4, x}, {y + 1/4, 
              x + 1/4, \(-z\) + 1/2}, {\(-y\), \(-x\) + 1/2, \(-z\)}\ 1, {y + 
                3/4, \(-x\), z + 1/4}, {\(-y\) + 1/2, x + 3/4, 
              z + 3/4}, {x + 1/4, z + 1/4, \(-y\) + 1/2}, {\(-x\) + 1/2, 
              z + 3/4, 
              y + 3/4}, {\(-x\), \(-z\) + 1/2, \(-y\)}, {x + 3/4, \(-z\), 
              y + 1/4}, {z + 1/4, y + 1/4, \(-x\) + 1/2}, {z + 3/4, \(-y\), 
              x + 1/4}, {\(-z\) + 1/2, y + 3/4, 
              x + 3/4}, {\(-z\), \(-y\) + 1/2, \(-x\)}\ 1, {\(-x\) + 
                1/2, \(-y\), \(-z\) + 1/2}, {x + 1/4, 
              y + 1/4, \(-z\)}, {x + 3/4, \(-y\) + 1/2, z + 1/4}, {\(-x\), 
              y + 3/4, 
              z + 3/4}, {\(-z\) + 1/2, \(-x\), \(-y\) + 1/2}, {\(-z\), 
              x + 3/4, y + 3/4}, {z + 1/4, 
              x + 1/4, \(-y\)}, {z + 3/4, \(-x\) + 1/2, 
              y + 1/4}, {\(-y\) + 1/2, \(-z\), \(-x\) + 
                1/2}, {y + 3/4, \(-z\) + 1/2, x + 1/4}\ 1, {\(-y\), z + 3/4, 
              x + 3/4}, {y + 1/4, 
              z + 1/4, \(-x\)}, {\(-y\) + 3/4, \(-x\) + 3/4, z + 1/2}, {y, 
              x + 1/2, z}, {\(-y\) + 1/4, 
              x, \(-z\) + 3/4}, {y + 1/2, \(-x\) + 1/4, \(-z\) + 
                1/4}, {\(-x\) + 3/4, \(-z\) + 3/4, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/4, \(-y\) + 1/4}, {x, z + 1/2, 
              y}, {\(-x\) + 1/4, z, \(-y\) + 3/4}\ 1, {\(-z\) + 3/4, \(-y\) + 
                3/4, x + 1/2}, {\(-z\) + 1/4, 
              y, \(-x\) + 3/4}, {z + 1/2, \(-y\) + 1/4, \(-x\) + 1/4}, {z, 
              y + 1/2, x}, {x + 1/2, y + 1/2, 
              z}, {\(-x\) + 3/4, \(-y\) + 1/4, z + 1/2}, {\(-x\) + 1/4, 
              y, \(-z\) + 1/4}, {x, \(-y\) + 3/4, \(-z\) + 3/4}, {z + 1/2, 
              x + 1/2, 
              y}, {z, \(-x\) + 3/4, \(-y\) + 3/4}\ 1, {\(-z\) + 3/4, \(-x\) + 
                1/4, y + 1/2}, {\(-z\) + 1/4, x, \(-y\) + 1/4}, {y + 1/2, 
              z + 1/2, x}, {\(-y\) + 1/4, 
              z, \(-x\) + 1/4}, {y, \(-z\) + 3/4, \(-x\) + 3/4}, {\(-y\) + 
                3/4, \(-z\) + 1/4, x + 1/2}, {y + 1/4, 
              x + 3/4, \(-z\)}, {\(-y\), \(-x\), \(-z\) + 1/2}, {y + 
                3/4, \(-x\) + 1/2, 
              z + 3/4}, {\(-y\) + 1/2, x + 1/4, z + 1/4}\ 1, {x + 1/4, 
              z + 3/4, \(-y\)}, {\(-x\) + 1/2, z + 1/4, 
              y + 1/4}, {\(-x\), \(-z\), \(-y\) + 1/2}, {x + 3/4, \(-z\) + 
                1/2, y + 3/4}, {z + 1/4, 
              y + 3/4, \(-x\)}, {z + 3/4, \(-y\) + 1/2, 
              x + 3/4}, {\(-z\) + 1/2, y + 1/4, 
              x + 1/4}, {\(-z\), \(-y\), \(-x\) + 1/2}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\)}, {x + 1/4, 
                y + 3/4, \(-z\) + 1/2}\ 1, {x + 3/4, \(-y\), 
              z + 3/4}, {\(-x\), y + 1/4, 
              z + 1/4}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\), 
              x + 1/4, y + 1/4}, {z + 1/4, 
              x + 3/4, \(-y\) + 1/2}, {z + 3/4, \(-x\), 
              y + 3/4}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\)}, {y + 
                3/4, \(-z\), x + 3/4}, {\(-y\), z + 1/4, 
              x + 1/4}, {y + 1/4, z + 3/4, \(-x\) + 1/2}\ 1, {\(-y\) + 
                3/4, \(-x\) + 1/4, z}, {y, x, z + 1/2}, {\(-y\) + 1/4, 
              x + 1/2, \(-z\) + 1/4}, {y + 1/2, \(-x\) + 3/4, \(-z\) + 
                3/4}, {\(-x\) + 3/4, \(-z\) + 1/4, 
              y}, {x + 1/2, \(-z\) + 3/4, \(-y\) + 3/4}, {x, z, 
              y + 1/2}, {\(-x\) + 1/4, 
              z + 1/2, \(-y\) + 1/4}, {\(-z\) + 3/4, \(-y\) + 1/4, 
              x}, {\(-z\) + 1/4, y + 1/2, \(-x\) + 1/4}\ 1, {z + 
                1/2, \(-y\) + 3/4, \(-x\) + 3/4}, {z, y, 
              x + 1/2}}, {"229 (Im-3m)", {x, y, z}, {\(-x\), \(-y\), 
              z}, {\(-x\), y, \(-z\)}, {x, \(-y\), \(-z\)}, {z, x, 
              y}, {z, \(-x\), \(-y\)}, {\(-z\), \(-x\), y}, {\(-z\), 
              x, \(-y\)}, {y, z, x}, {\(-y\), 
              z, \(-x\)}, {y, \(-z\), \(-x\)}, {\(-y\), \(-z\), x}, {y, 
              x, \(-z\)}, {\(-y\), \(-x\), \(-z\)}, {y, \(-x\), z}, {\(-y\), 
              x, z}, {x, z, \(-y\)}, {\(-x\), z, 
              y}, {\(-x\), \(-z\), \(-y\)}, {x, \(-z\), y}, {z, 
              y, \(-x\)}, {z, \(-y\), x}, {\(-z\), y, 
              x}, {\(-z\), \(-y\), \(-x\)}, {\(-x\), \(-y\), \(-z\)}, {x, 
              y, \(-z\)}, {x, \(-y\), z}, {\(-x\), y, 
              z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\), x, y}, {z, 
              x, \(-y\)}, {z, \(-x\), 
              y}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\), x}, {\(-y\), z, 
              x}, {y, z, \(-x\)}, {\(-y\), \(-x\), z}, {y, x, z}, {\(-y\), 
              x, \(-z\)}, {y, \(-x\), \(-z\)}, {\(-x\), \(-z\), 
              y}, {x, \(-z\), \(-y\)}, {x, z, y}, {\(-x\), 
              z, \(-y\)}, {\(-z\), \(-y\), x}, {\(-z\), 
              y, \(-x\)}, {z, \(-y\), \(-x\)}, {z, y, x}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\) + 
                1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, \(-x\) + 1/2, y + 1/2}, {\(-z\) + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 1/2, \(-x\) + 
                1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, x + 1/2}, {y + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {y + 1/2, \(-x\) + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, z + 1/2}, {x + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-x\) + 1/2, z + 1/2, 
              y + 1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 
                1/2, \(-z\) + 1/2, y + 1/2}, {z + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, y + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, \(-x\) + 1/2}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x + 1/2, 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, 
              z + 1/2}, {\(-x\) + 1/2, y + 1/2, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\) + 
                1/2, x + 1/2, y + 1/2}, {z + 1/2, 
              x + 1/2, \(-y\) + 1/2}, {z + 1/2, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                1/2, \(-z\) + 1/2, x + 1/2}, {\(-y\) + 1/2, z + 1/2, 
              x + 1/2}, {y + 1/2, 
              z + 1/2, \(-x\) + 1/2}, {\(-y\) + 1/2, \(-x\) + 1/2, 
              z + 1/2}, {y + 1/2, x + 1/2, z + 1/2}, {\(-y\) + 1/2, 
              x + 1/2, \(-z\) + 1/2}, {y + 1/2, \(-x\) + 1/2, \(-z\) + 
                1/2}, {\(-x\) + 1/2, \(-z\) + 1/2, 
              y + 1/2}, {x + 1/2, \(-z\) + 1/2, \(-y\) + 1/2}, {x + 1/2, 
              z + 1/2, y + 1/2}, {\(-x\) + 1/2, 
              z + 1/2, \(-y\) + 1/2}, {\(-z\) + 1/2, \(-y\) + 1/2, 
              x + 1/2}, {\(-z\) + 1/2, 
              y + 1/2, \(-x\) + 1/2}, {z + 1/2, \(-y\) + 1/2, \(-x\) + 
                1/2}, {z + 1/2, y + 1/2, x + 1/2}}, {"230 (Ia-3d)", {x, 
              y, z}, {\(-x\) + 1/2, \(-y\), z + 1/2}, {\(-x\), 
              y + 1/2, \(-z\) + 1/2}, {x + 1/2, \(-y\) + 1/2, \(-z\)}, {z, x, 
              y}, {z + 1/2, \(-x\) + 1/2, \(-y\)}, {\(-z\) + 1/2, \(-x\), 
              y + 1/2}, {\(-z\), x + 1/2, \(-y\) + 1/2}, {y, z, x}, {\(-y\), 
              z + 1/2, \(-x\) + 1/2}, {y + 1/2, \(-z\) + 
                1/2, \(-x\)}, {\(-y\) + 1/2, \(-z\), x + 1/2}, {y + 3/4, 
              x + 1/4, \(-z\) + 1/4}, {\(-y\) + 3/4, \(-x\) + 3/4, \(-z\) + 
                3/4}, {y + 1/4, \(-x\) + 1/4, z + 3/4}, {\(-y\) + 1/4, 
              x + 3/4, z + 1/4}, {x + 3/4, 
              z + 1/4, \(-y\) + 1/4}, {\(-x\) + 1/4, z + 3/4, 
              y + 1/4}, {\(-x\) + 3/4, \(-z\) + 3/4, \(-y\) + 3/4}, {x + 
                1/4, \(-z\) + 1/4, y + 3/4}, {z + 3/4, 
              y + 1/4, \(-x\) + 1/4}, {z + 1/4, \(-y\) + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, y + 3/4, 
              x + 1/4}, {\(-z\) + 3/4, \(-y\) + 3/4, \(-x\) + 
                3/4}, {\(-x\), \(-y\), \(-z\)}, {x + 1/2, 
              y, \(-z\) + 1/2}, {x, \(-y\) + 1/2, z + 1/2}, {\(-x\) + 1/2, 
              y + 1/2, z}, {\(-z\), \(-x\), \(-y\)}, {\(-z\) + 1/2, x + 1/2, 
              y}, {z + 1/2, x, \(-y\) + 1/2}, {z, \(-x\) + 1/2, 
              y + 1/2}, {\(-y\), \(-z\), \(-x\)}, {y, \(-z\) + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, z + 1/2, x}, {y + 1/2, 
              z, \(-x\) + 1/2}, {\(-y\) + 1/4, \(-x\) + 3/4, 
              z + 3/4}, {y + 1/4, x + 1/4, z + 1/4}, {\(-y\) + 3/4, 
              x + 3/4, \(-z\) + 1/4}, {y + 3/4, \(-x\) + 1/4, \(-z\) + 
                3/4}, {\(-x\) + 1/4, \(-z\) + 3/4, 
              y + 3/4}, {x + 3/4, \(-z\) + 1/4, \(-y\) + 3/4}, {x + 1/4, 
              z + 1/4, y + 1/4}, {\(-x\) + 3/4, 
              z + 3/4, \(-y\) + 1/4}, {\(-z\) + 1/4, \(-y\) + 3/4, 
              x + 3/4}, {\(-z\) + 3/4, 
              y + 3/4, \(-x\) + 1/4}, {z + 3/4, \(-y\) + 1/4, \(-x\) + 
                3/4}, {z + 1/4, y + 1/4, x + 1/4}, {x + 1/2, y + 1/2, 
              z + 1/2}, {\(-x\), \(-y\) + 1/2, z}, {\(-x\) + 1/2, 
              y, \(-z\)}, {x, \(-y\), \(-z\) + 1/2}, {z + 1/2, x + 1/2, 
              y + 1/2}, {z, \(-x\), \(-y\) + 1/2}, {\(-z\), \(-x\) + 1/2, 
              y}, {\(-z\) + 1/2, x, \(-y\)}, {y + 1/2, z + 1/2, 
              x + 1/2}, {\(-y\) + 1/2, 
              z, \(-x\)}, {y, \(-z\), \(-x\) + 1/2}, {\(-y\), \(-z\) + 1/2, 
              x}, {y + 1/4, 
              x + 3/4, \(-z\) + 3/4}, {\(-y\) + 1/4, \(-x\) + 1/4, \(-z\) + 
                1/4}, {y + 3/4, \(-x\) + 3/4, z + 1/4}, {\(-y\) + 3/4, 
              x + 1/4, z + 3/4}, {x + 1/4, 
              z + 3/4, \(-y\) + 3/4}, {\(-x\) + 3/4, z + 1/4, 
              y + 3/4}, {\(-x\) + 1/4, \(-z\) + 1/4, \(-y\) + 1/4}, {x + 
                3/4, \(-z\) + 3/4, y + 1/4}, {z + 1/4, 
              y + 3/4, \(-x\) + 3/4}, {z + 3/4, \(-y\) + 3/4, 
              x + 1/4}, {\(-z\) + 3/4, y + 1/4, 
              x + 3/4}, {\(-z\) + 1/4, \(-y\) + 1/4, \(-x\) + 1/4}, {\(-x\) + 
                1/2, \(-y\) + 1/2, \(-z\) + 1/2}, {x, 
              y + 1/2, \(-z\)}, {x + 1/2, \(-y\), z}, {\(-x\), y, 
              z + 1/2}, {\(-z\) + 1/2, \(-x\) + 1/2, \(-y\) + 1/2}, {\(-z\), 
              x, y + 1/2}, {z, x + 1/2, \(-y\)}, {z + 1/2, \(-x\), 
              y}, {\(-y\) + 1/2, \(-z\) + 1/2, \(-x\) + 1/2}, {y + 
                1/2, \(-z\), x}, {\(-y\), z, x + 1/2}, {y, 
              z + 1/2, \(-x\)}, {\(-y\) + 3/4, \(-x\) + 1/4, 
              z + 1/4}, {y + 3/4, x + 3/4, z + 3/4}, {\(-y\) + 1/4, 
              x + 1/4, \(-z\) + 3/4}, {y + 1/4, \(-x\) + 3/4, \(-z\) + 
                1/4}, {\(-x\) + 3/4, \(-z\) + 1/4, 
              y + 1/4}, {x + 1/4, \(-z\) + 3/4, \(-y\) + 1/4}, {x + 3/4, 
              z + 3/4, y + 3/4}, {\(-x\) + 1/4, 
              z + 1/4, \(-y\) + 3/4}, {\(-z\) + 3/4, \(-y\) + 1/4, 
              x + 1/4}, {\(-z\) + 1/4, 
              y + 1/4, \(-x\) + 3/4}, {z + 1/4, \(-y\) + 3/4, \(-x\) + 
                1/4}, {z + 3/4, y + 3/4, x + 3/4}}};\)\)\)

Utility Functions

Convestion between Vector Form and Affine Matrix Form

VectorToAffineMatrix[v_List] := {Map[Coefficient[#, {x, y, z}] &, v], 
          ReplaceAll[
            v, {x -> 0, y -> 0, z -> 0}]};
VectorToTransMatrix[v_List] := 
        If[ReplaceAll[
              v, {x -> 0, y -> 0, z -> 0}] == {0, 0, 0}, 
          Map[Coefficient[#, {x, y, z}] &, v], {}];

Correspondence Table between Point Groups and Space Groups

SubsetQ[child_, parent_] := 
        If[Length[Intersection[Union[child], Union[parent]]] == 
            Length[Union[child]], True, False];
PointGroupInSpaceGroupQ[point_, space_] := 
        SubsetQ[Map[VectorToTransMatrix, point], 
          Map[VectorToTransMatrix, space]];
CorrespondenceTable = {};
Do[{result = {}; 
TestPointGroup = 
            Drop[PointGroupOperations[[i]], 1]; 
Do[
            If[PointGroupInSpaceGroupQ[TestPointGroup, 
                Drop[SpaceGroupOperations[[j]], 1]], 
              AppendTo[
                result, SpaceGroupOperations[[j]][[1]]]], {j, 
              Length[SpaceGroupOperations]}]; 
AppendTo[
            CorrespondenceTable, {PointGroupOperations[[i]][[1]], 
              result}]}, {i, Length[PointGroupOperations]}];
CorrespondenceTable // TraditionalForm
CorrespondenceTableInReverseOrder = 
        MapAt[Reverse, CorrespondenceTable, 
          Table[{i, 2}, {i, 
              Length[CorrespondenceTable]}]];
CorrespondenceTableInReverseOrder // 
      TraditionalForm

Conversion between Hexagonal Axes' Form and Rhombohedral Axes' Form

(*
Input :  
        a and c in the hexagonal axes unit cell; 
Output :  
        a and alpha (in Degree) in the rhombohedral axes unit cell.
*) 
HexagonalToRhombohedralUnitCell[a_, c_] := {Sqrt[3  a*a + c*c]/3, 
          2  ArcSin[3/(2  Sqrt[3 + (c/a)^2])]/
              Degree};

 (*Transformation matrix between the two unit cells*) 

    RtoHmatrix = {{2/3, -1/3, -1/3}, {1/3, 1/3, -2/3}, {1/3, 1/3, 
          1/3}}

    HtoRmatrix = Inverse[RtoHmatrix]

References

Source:Bilbao Crystallographic Server bcs Point Group Tables.
See:M.I.Aroyo,A.Kirov,C.Capillas,J.M.Perez-Mato& H.Wondratschek."Bilbao Crystallographic Server II: Representations of crystallographic point groups and space groups".Acta Cryst.(2006),A62,115-128.
Aroyo et al."Bilbao Crystallographic Server: Databases and crystallographic computing programs".Zeitschrift fuer Kristallographie,(2006),221,1,015-027.
http://www.cryst.ehu.es/index.html#retrieval.Access Date:July 05,2006.