User:Tomruen/hyperbolic honeycombs
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
[edit]Here 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)
| ||