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)