Polytope families
contrast and colors . (March 2021) |
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 |
Demitesseract
|
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 |
Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn
| |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform polychoron
|
Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: Polytope families • List of regular polytopes and compounds
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