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 | ||||||||||||||||
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Family n |
n-simplex | n-hypercube | n-orthoplex | n-demicube | 1k2 | 2k1 | k21 | pentagonal polytope | ||||||||
Group | An | Bn |
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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 |
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6 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-simplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-cube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-orthoplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 6-demicube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 122 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 221 |
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7 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-simplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-cube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-orthoplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 7-demicube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 132 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 231 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 321 |
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8 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-simplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-cube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-orthoplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 8-demicube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 142 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 241 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 421 |
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9 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-simplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-cube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-orthoplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 9-demicube |
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10 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-simplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-cube |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-orthoplex |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() 10-demicube |