Overview
- Group
- SmallGroup(896,19344)
- Rank
- 3
- Schläfli Type
- {4,7}
- Vertices, edges, …
- 64, 224, 112
- Order of s0s1s2
- 7
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3*s1> of order 2
64 facets
32 vertex figures
- 32 of {7}*14
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 2
56 facets
- 56 of {4}*8
32 vertex figures
- 32 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
56 facets
- 56 of {4}*8
32 vertex figures
- 32 of {7}*14
P/N, where N=<s0*(s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 2
56 facets
- 56 of {4}*8
32 vertex figures
- 32 of {7}*14
P/N, where N=<(s0*s1)^2*(s2*s1)^3*s0*(s1*s2)^3> of order 2
56 facets
- 56 of {4}*8
32 vertex figures
- 32 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*(s1*s2)^2*s1)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2> of order 4
36 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*(s1*s2)^2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*(s1*s2)^2*s1)^2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s1*s0*(s1*s2)^2)^2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3*s1> of order 4
36 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s0*(s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s0*(s1*s2)^3)^2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*(s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2, s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
32 facets
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s0*s1*(s2*s1*s0)^3*s1*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s1*s0*s1*s2)^2, s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1> of order 4
28 facets
- 28 of {4}*8
16 vertex figures
- 16 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 8
20 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*(s1*s2)^2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*(s1*s2)^2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, (s0*(s1*s2)^2*s1)^2> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*(s1*s2)^2*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*(s1*s2)^2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*(s1*s2)^2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^2*s1*(s0*(s2*s1)^2)^2*s2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*(s2*s1)^3*s0*s1*s2, s0*s1*(s2*s1*s0)^3*s1*s2> of order 8
14 facets
- 14 of {4}*8
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*(s1*s2)^2*s1)^2, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
18 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s1*s2> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2, (s0*(s1*s2)^2*s1)^2> of order 8
20 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
16 facets
8 vertex figures
- 8 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 16
11 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 16
10 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 16
9 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1, (s0*(s1*s2)^2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 16
9 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 16
9 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16
7 facets
- 7 of {4}*8
4 vertex figures
- 4 of {7}*14
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 16
8 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, (s0*(s1*s2)^2*s1)^2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 16
10 facets
4 vertex figures
- 4 of {7}*14
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16
10 facets
4 vertex figures
- 4 of {7}*14
Representations
Permutation Representation (GAP)
s0 := ( 1,37)( 2,38)( 3,39)( 4,40)( 5,33)( 6,34)( 7,35)( 8,36)( 9,45)(10,46)(11,47)(12,48)(13,41)(14,42)(15,43)(16,44)(17,53)(18,54)(19,55)(20,56)(21,49)(22,50)(23,51)(24,52)(25,61)(26,62)(27,63)(28,64)(29,57)(30,58)(31,59)(32,60);; s1 := ( 2,49)( 3,17)( 4,33)( 5,25)( 6,41)( 7, 9)( 8,57)(10,55)(11,23)(12,39)(13,31)(14,47)(16,63)(18,51)(20,35)(21,27)(22,43)(24,59)(26,53)(28,37)(30,45)(32,61)(34,52)(38,44)(40,60)(42,54)(48,62)(56,58);; s2 := ( 2,57)( 3,49)( 4, 9)( 5,33)( 6,25)( 7,17)( 8,41)(10,60)(11,52)(13,36)(14,28)(15,20)(16,44)(18,63)(19,55)(21,39)(22,31)(24,47)(26,62)(27,54)(29,38)(32,46)(34,61)(35,53)(40,45)(42,64)(43,56)(50,59);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!( 1,37)( 2,38)( 3,39)( 4,40)( 5,33)( 6,34)( 7,35)( 8,36)( 9,45)(10,46)(11,47)(12,48)(13,41)(14,42)(15,43)(16,44)(17,53)(18,54)(19,55)(20,56)(21,49)(22,50)(23,51)(24,52)(25,61)(26,62)(27,63)(28,64)(29,57)(30,58)(31,59)(32,60); s1 := Sym(64)!( 2,49)( 3,17)( 4,33)( 5,25)( 6,41)( 7, 9)( 8,57)(10,55)(11,23)(12,39)(13,31)(14,47)(16,63)(18,51)(20,35)(21,27)(22,43)(24,59)(26,53)(28,37)(30,45)(32,61)(34,52)(38,44)(40,60)(42,54)(48,62)(56,58); s2 := Sym(64)!( 2,57)( 3,49)( 4, 9)( 5,33)( 6,25)( 7,17)( 8,41)(10,60)(11,52)(13,36)(14,28)(15,20)(16,44)(18,63)(19,55)(21,39)(22,31)(24,47)(26,62)(27,54)(29,38)(32,46)(34,61)(35,53)(40,45)(42,64)(43,56)(50,59); poly := sub<Sym(64)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;
References
None.
to this polytope.