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
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)![]() |