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User:Tomruen/hyperbolic honeycombs

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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)