User:Tomruen/Uniform polyhedron table
Table of vertex figures for Wythoff sets on the sphere
| (p q r) | q|pr | p|qr | r|pq | qr|p | pr|q | qp|r | pqr| | |pqr | |
|---|---|---|---|---|---|---|---|---|---|
| dihedral | |||||||||
| (2 2 2) | [di:(2)^2] | - | - | [hos:4.4] | - | - | 4.4.4 | 3.3.3 | |
| (3 2 2) | [di:(3)^2] | [di:(2)^3] | - | [hos:6.6] | 3.4.4 | - | 6.4.4 | 3.3.3.3 | |
| (4 2 2) | [di:(4)^2] | [di:(2)^4] | - | [hos:8.8] | 4.4.4 | - | 8.4.4 | 3.3.3.4 | |
| (5 2 2) | [di:(5)^2] | [di:(2)^5] | - | [hos:10.10] | 5.4.4 | - | 10.4.4 | 3.3.3.5 | |
| (6 2 2) | [di:(6)^2] | [di:(2)^6] | - | [hos:12.12] | 6.4.4 | - | 12.4.4 | 3.3.3.6 | |
| (7 2 2) | [di:(7)^2] | [di:(2)^7] | - | [hos:14.14] | 7.4.4 | - | 14.4.4 | 3.3.3.7 | |
| (8 2 2) | [di:(8)^2] | [di:(2)^8] | - | [hos:16.16] | 8.4.4 | - | 16.4.4 | 3.3.3.8 | |
| (9 2 2) | [di:(9)^2] | [di:(2)^9] | - | [hos:18.18] | 9.4.4 | - | 18.4.4 | 3.3.3.9 | |
| (10 2 2) | [di:(10)^2] | [di:(2)^10] | - | [hos:20.20] | 10.4.4 | - | 20.4.4 | 3.3.3.10 | |
| (11 2 2) | [di:(11)^2] | [di:(2)^11] | - | [hos:22.22] | 11.4.4 | - | 22.4.4 | 3.3.3.11 | |
| (12 2 2) | [di:(12)^2] | [di:(2)^12] | - | [hos:24.24] | 12.4.4 | - | 24.4.4 | 3.3.3.12 | |
| Tetrahedral | |||||||||
| (3 3 2) | (3)^3 | - | (3.3)^2 | 3.6.6 | - | 3.4.3.4 | 6.6.4 | 3.3.3.3.3 | |
| Octahedral | |||||||||
| (4 3 2) | (4)^3 | (3)^4 | (4.3)^2 | 3.8.8 | 4.6.6 | 3.4.4.4 | 8.6.4 | 3.3.3.3.4 | |
| Icosahedral | |||||||||
| (5 3 2) | (5)^3 | (3)^5 | (5.3)^2 | 3.10.10 | 5.6.6 | 3.4.5.4 | 10.6.4 | 3.3.3.3.5 | |
| dihedral nonconvex | |||||||||
| (5/2 2 2) | [di:(5/2)^2] | [di:(2)^5/2] | - | [hos:5.5] | 5/2.4.4 | - | 5.4.4 | 3.3.3.5/2 | |
| (7/2 2 2) | [di:(7/2)^2] | [di:(2)^7/2] | - | [hos:7.7] | 7/2.4.4 | - | 7.4.4 | 3.3.3.7/2 | |
| (7/3 2 2) | [di:(7/3)^2] | [di:(2)^7/3] | - | [hos:14/3.14/3] | 7/3.4.4 | - | 14/3.4.4 | 3.3.3.7/3 | |
| (8/3 2 2) | [di:(8/3)^2] | [di:(2)^8/3] | - | [hos:16/3.16/3] | 8/3.4.4 | - | 16/3.4.4 | 3.3.3.8/3 | |
| (9/2 2 2) | [di:(9/2)^2] | [di:(2)^9/2] | - | [hos:9.9] | 9/2.4.4 | - | 9.4.4 | 3.3.3.9/2 | |
| (9/4 2 2) | [di:(9/4)^2] | [di:(2)^9/4] | - | [hos:9/2.9/2] | 9/4.4.4 | - | 9/2.4.4 | 3.3.3.9/4 | |
| (10/3 2 2) | [di:(10/3)^2] | [di:(2)^10/3] | - | [hos:20/3.20/3] | 10/3.4.4 | - | 20/3.4.4 | 3.3.3.10/3 | |
| (11/2 2 2) | [di:(11/2)^2] | [di:(2)^11/2] | - | [hos:11.11] | 11/2.4.4 | - | 11.4.4 | 3.3.3.11/2 | |
| (11/3 2 2) | [di:(11/3)^2] | [di:(2)^11/3] | - | [hos:22/3.22/3] | 11/3.4.4 | - | 22/3.4.4 | 3.3.3.11/3 | |
| (11/4 2 2) | [di:(11/4)^2] | [di:(2)^11/4] | - | [hos:11/2.11/2] | 11/4.4.4 | - | 11/2.4.4 | 3.3.3.11/4 | |
| (11/5 2 2) | [di:(11/5)^2] | [di:(2)^11/5] | - | [hos:22/5.22/5] | 11/5.4.4 | - | 22/5.4.4 | 3.3.3.11/5 | |
| (12/5 2 2) | [di:(12/5)^2] | [di:(2)^12/5] | - | [hos:24/5.24/5] | 12/5.4.4 | - | 24/5.4.4 | 3.3.3.12/5 | |
| tetrahedral nonconvex | |||||||||
| (3 3/2 2) | (3)^3/2 | (3/2)^3 | (3.3/2)^2 | 3/2.6.6 | 3.3.3 | 3/2.4.3.4 | 6.3.4 | 3.3.3/2.3.3 | |
| (3 3 3/2) | (3.3/2)^3 | - | - | 3.6.3/2.6 | - | 3.3.3.3 | 6.6.3 | 3.3/2.3.3.3.3 | |
| Octahedra nonconvex | |||||||||
| (4/3 3 2) | (4/3)^3 | (3)^4/3 | (4/3.3)^2 | 3.8/3.8/3 | 4/3.6.6 | 3.4.4/3.4 | 8/3.6.4 | 3.3.3.3.4/3 | |
| (4 4/3 4) | (4.4)^4/3 | (4/3.4)^4 | (4.4/3)^4 | 4/3.8.4.8 | 4.8/3.4.8/3 | - | 8.8/3.8 | 3.4.3.4/3.3.4 | |
| (4 4 3/2) | (4.3/2)^4 | - | (4.4)^3/2 | 4.8.3/2.8 | - | 4.3.4.3 | 8.8.3 | 3.3/2.3.4.3.4 | |
| (4 3/2 2) | (4)^3/2 | (3/2)^4 | (4.3/2)^2 | 3/2.8.8 | 4.3.3 | 3/2.4.4.4 | 8.3.4 | 3.3.3/2.3.4 | |
| (4/3 3/2 2) | (4/3)^3/2 | (3/2)^4/3 | (4/3.3/2)^2 | 3/2.8/3.8/3 | 4/3.3.3 | 3/2.4.4/3.4 | 8/3.3.4 | 3.3.3/2.3.4/3 | |
| (4 4 3/2) | (4.3/2)^4 | - | (4.4)^3/2 | 4.8.3/2.8 | - | 4.3.4.3 | 8.8.3 | 3.3/2.3.4.3.4 | |
| Icosahedra nonconvex | |||||||||
| (5/2 3 2) | (5/2)^3 | (3)^5/2 | (5/2.3)^2 | 3.5.5 | 5/2.6.6 | 3.4.5/2.4 | 5.6.4 | 3.3.3.3.5/2 | |
| (5 5/2 2) | (5)^5/2 | (5/2)^5 | (5.5/2)^2 | 5/2.10.10 | 5.5.5 | 5/2.4.5.4 | 10.5.4 | 3.3.5/2.3.5 | |
| (5/2 3 3) | (5/2.3)^3 | (3.3)^5/2 | - | 3.5.3.5 | 5/2.6.3.6 | - | 5.6.6 | 3.3.3.3.3.5/2 | |
| (5 5/3 2) | (5)^5/3 | (5/3)^5 | (5.5/3)^2 | 5/3.10.10 | 5.10/3.10/3 | 5/3.4.5.4 | 10.10/3.4 | 3.3.5/3.3.5 | |
| (5/3 3 2) | (5/3)^3 | (3)^5/3 | (5/3.3)^2 | 3.10/3.10/3 | 5/3.6.6 | 3.4.5/3.4 | 10/3.6.4 | 3.3.3.3.5/3 | |
| (5 3 3/2) | (5.3/2)^3 | (3.3/2)^5 | (5.3)^3/2 | 3.10.3/2.10 | 5.6.3/2.6 | 3.3.5.3 | 10.6.3 | 3.3/2.3.3.3.5 | |
| (5 5 5/4) | (5.5/4)^5 | - | - | 5.10.5/4.10 | - | 5.5/2.5.5/2 | 10.10.5/2 | 3.5/4.3.5.3.5 | |
| (5/3 3 3) | (5/3.3)^3 | (3.3)^5/3 | - | 3.10/3.3.10/3 | 5/3.6.3.6 | - | 10/3.6.6 | 3.3.3.3.3.5/3 | |
| (5/2 5/3 5/3) | (5/2.5/3)^5/3 | (5/3.5/3)^5/2 | - | 5/3.5.5/3.5 | 5/2.10/3.5/3.10/3 | - | 5.10/3.10/3 | 3.5/3.3.5/3.3.5/2 | |
| (5 5/4 3) | (5.3)^5/4 | (5/4.3)^5 | (5.5/4)^3 | 5/4.10.3.10 | 5.5/2.3.5/2 | 5/4.6.5.6 | 10.5/2.6 | 3.3.3.5/4.3.5 | |
| (5/2 5/3 3) | (5/2.3)^5/3 | (5/3.3)^5/2 | (5/2.5/3)^3 | 5/3.5.3.5 | 5/2.10/3.3.10/3 | 5/3.6.5/2.6 | 5.10/3.6 | 3.3.3.5/3.3.5/2 | |
| (5 5 3/2) | (5.3/2)^5 | - | (5.5)^3/2 | 5.10.3/2.10 | - | 5.3.5.3 | 10.10.3 | 3.3/2.3.5.3.5 | |
| (5 5/3 3) | (5.3)^5/3 | (5/3.3)^5 | (5.5/3)^3 | 5/3.10.3.10 | 5.10/3.3.10/3 | 5/3.6.5.6 | 10.10/3.6 | 3.3.3.5/3.3.5 | |
| (5/3 3/2 2) | (5/3)^3/2 | (3/2)^5/3 | (5/3.3/2)^2 | 3/2.10/3.10/3 | 5/3.3.3 | 3/2.4.5/3.4 | 10/3.3.4 | 3.3.3/2.3.5/3 | |
| (5/2 3/2 3/2) | (5/2.3/2)^3/2 | (3/2.3/2)^5/2 | - | 3/2.5.3/2.5 | 5/2.3.3/2.3 | - | 5.3.3 | 3.3/2.3.3/2.3.5/2 | |
| (5 3 3/2) | (5.3/2)^3 | (3.3/2)^5 | (5.3)^3/2 | 3.10.3/2.10 | 5.6.3/2.6 | 3.3.5.3 | 10.6.3 | 3.3/2.3.3.3.5 | |