This content is now 100% moved to:Convex_uniform_honeycombs_in_hyperbolic_space, and I'll finish work there. Tom Ruen (talk) 22:10, 2 January 2009 (UTC)
New non-wythoff section in progress. Tom Ruen (talk) 06:01, 12 January 2009 (UTC)
Vertex figures collected at: User:Tomruen/polychoron verf
Nonwythoffian forms
editHere are 7 sets uniform hyperbolic honeycombs that are non-Wythoffian (not constructed through mirror symmetry):
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| (p=2) | {4,3,4} |
Octahedron (Degenerate icosahedron) |
8 (4.4.4) |
||
| 1a (p=3) |
Icosahedron |
8 (4.4.4) |
12 (4.4.3) | ||
| (p=4) | {4,3,5} |
regular Icosahedron |
8 (4.4.4) |
12 (4.4.4) | |
| 1b (p=5) |
Icosahedron |
8 (4.4.4) |
12 (4.4.5) | ||
| 1c (p=6) p=6,7,8... |
Icosahedron |
8 (4.4.4) |
12 (4.4.6) | ||
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| (p=3) | 600-cell |
snub tetrahedron |
4 (3.3.3) |
4+12 (3.3.3) | |
| 2a (p=4) |
Snub cube |
6 (3.3.3.3) |
8+24 (3.3.3) | ||
| 2b (p=5) |
Snub dodecahedron |
12 (3.3.3.3.3) |
20+60 (3.3.3) | ||
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| (p=3) | Truncated 600-cell |
pentagonal pyramid |
4 (3.6.6) |
1 (3.6.6) |
1 (3.3.3.3.3) |
| 3a (p=4) |
pentagonal pyramid |
4 (3.6.6) |
1 (4.6.6) |
1 (3.3.3.3.4) | |
| 3b (p=5) |
pentagonal pyramid |
4 (3.6.6) |
1 (5.6.6) |
1 (3.3.3.3.5) | |
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| (p=3) | Rectified 600-cell |
uniform pentagonal prism |
1 (3.3.3.3) |
2 (3.3.3.3.3) |
4 (3.3.3.3) |
| 4a (p=4) |
pentagonal prism |
1 (3.4.3.4) |
2 (3.3.3.3.4) |
4 (3.3.3.3) | |
| 4b (p=5) |
Pentagonal prism |
1 (3.5.3.5) |
2 (3.3.3.3.5) |
4 (3.3.3.3) | |
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| {3,5,3} |
Dodecahedron |
12 (3.3.3.3.3) |
|||
| 5 | tetrahedrally-alternated dodecahedron |
12 (3.3.3.5) |
4 (5.5.5) | ||
| # | Name | Vertex figure |
Cells | ||
|---|---|---|---|---|---|
| 6 | octagonal bipyramid |
16 (3.8.8) | |||
| 7 | order-2 spherical polyhedron |
8+8 (3.4.4) |
8+8 (3.4.4.4) | ||
