Polytope families
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There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality. These are tabulated here with Petrie polygon projection graphs and Coxeter–Dynkin diagrams.
Table of irreducible polytope families | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Family n | n-simplex | n-hypercube | n-orthoplex | n-demicube | 1k2 | 2k1 | k21 | pentagonal polytope | ||||||||
Group | An | Bn |
|
| Hn | |||||||||||
2 | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() p-gon (example: p=7) | ![]() ![]() ![]() ![]() Hexagon | ![]() ![]() ![]() ![]() Pentagon | |||||||||||
3 | ![]() ![]() ![]() ![]() ![]() ![]() Tetrahedron | ![]() ![]() ![]() ![]() ![]() ![]() Cube | ![]() ![]() ![]() ![]() ![]() ![]() Octahedron | ![]() ![]() ![]() ![]() Tetrahedron | ![]() ![]() ![]() ![]() ![]() ![]() Dodecahedron | ![]() ![]() ![]() ![]() ![]() ![]() Icosahedron | ||||||||||
4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 5-cell | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 16-cell | ![]() ![]() ![]() ![]() ![]() ![]() | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 24-cell | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 120-cell | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 600-cell | |||||||||
5 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 5-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 5-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 5-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 5-demicube | ||||||||||||
6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-demicube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 122 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 221 | ||||||||||
7 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-demicube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 132 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 231 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 321 | |||||||||
8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-demicube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 142 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 241 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 421 | |||||||||
9 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-demicube | ||||||||||||
10 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-simplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-cube | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-orthoplex | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-demicube |