Polytope families
From Infogalactic: the planetary knowledge core
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.
| Family n |
n-simplex | n-hypercube | n-orthoplex | n-demicube | 1k2 | 2k1 | k21 | pentagonal polytope | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Group | An | BCn |
|
|
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 |
File:Gosset 1 32 petrie.svg 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 |
||||||||||||
| Fundamental convex regular and uniform polytopes in dimensions 2–10 | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 4-polytope | 5-cell | 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 • Regular polytope • List of regular polytopes and compounds | ||||||||||||
