This article or section uses
color as the only way to convey important information. (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 |
|
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 |
This article or section uses
color as the only way to convey important information. (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 |
|
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 |