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Making Polyhedra with Polyhedral Groups
Author

Ed Pegg
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Revision date

2003-03-14
Description

As mentioned under the Mathworld entry, Polyhedral Group, the platonic and archimedean solids all belong to one of three symmetry groups: Tetrahedral, Octahedral, or Icosahedral.

With these groups of rotation matrices, a single vector can be used to represent the snub cube, and many other solids.
Subjects

*Mathematica Technology > Programming > 3D Graphics
*Mathematics > Algebra > Group Theory
*Mathematics > Algebra > Linear Algebra
*Mathematics > Geometry > Solid Geometry
Keywords

Special orthogonal group, polyhedra, snub, rotation group, archimedean
URL

http://mathworld.wolfram.com/PolyhedralGroup.html
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PolyhedraMap.nb (43.9 KB) - Using Group Theory to make polyhedra