Overview
- Group
- SmallGroup(896,19344)
- Rank
- 3
- Schläfli Type
- {7,4}
- Vertices, edges, …
- 112, 224, 64
- 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
- Self-Petrie
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=<s0*s1*s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 2
32 facets
- 32 of {7}*14
56 vertex figures
- 56 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
36 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
36 vertex figures
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2, (s0*s1)^3*s2*(s1*s0)^3*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^2*s0*s2*(s1*s0)^2*(s2*s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^3*s2, s0*s1*s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<((s1*s0)^2*s1*s2)^2, (s0*s1)^3*s0*s2*(s1*s0)^3*s2*s1*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2> of order 4
16 facets
- 16 of {7}*14
36 vertex figures
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2*s1*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0*s1*s2*s1, (s0*s1)^2*s2*s1*s0*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<(s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2*s2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
16 facets
- 16 of {7}*14
32 vertex figures
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2> of order 4
16 facets
- 16 of {7}*14
28 vertex figures
- 28 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, ((s1*s0)^2*s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0*s1*s2)^2, ((s1*s0)^2*s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, ((s1*s0)^2*s1*s2)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2, ((s1*s0)^2*s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s1*s2)^2, (s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2> of order 8
8 facets
- 8 of {7}*14
20 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^3*s0*s2*(s1*s0)^3*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, ((s1*s0)^2*s1*s2)^2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s0*s1)^2*s2*(s1*s0)^2*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 8
8 facets
- 8 of {7}*14
20 vertex figures
P/N, where N=<(s1*s2)^2, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, ((s1*s0)^2*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s1*s2)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s1*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2, (s0*s1)^3*s2*(s1*s0)^3*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, ((s1*s0)^2*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s2, (s0*s1)^3*s2*(s1*s0)^3*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s2, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, ((s1*s0)^2*s1*s2)^2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^3*s2*s1*s0*s2*(s1*s0)^2*s2, (s0*s1)^2*s0*(s2*(s1*s0)^2)^2*s1> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^3*s0*s2*s1*s0*s2*(s1*s0)^2*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, ((s1*s0)^2*s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2, (s0*s1)^3*s2*(s1*s0)^3*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 8
8 facets
- 8 of {7}*14
18 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0> of order 8
8 facets
- 8 of {7}*14
20 vertex figures
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 8
8 facets
- 8 of {7}*14
14 vertex figures
- 14 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2, ((s1*s0)^2*s1*s2)^2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2, (s0*s1)^3*s2*(s1*s0)^3*s2> of order 8
8 facets
- 8 of {7}*14
16 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2> of order 16
4 facets
- 4 of {7}*14
9 vertex figures
P/N, where N=<(s1*s2)^2, (s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2, (s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0> of order 16
4 facets
- 4 of {7}*14
11 vertex figures
P/N, where N=<(s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 16
4 facets
- 4 of {7}*14
8 vertex figures
P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^3*s0*s2*(s1*s0)^2*s2*s1*s0*s1> of order 16
4 facets
- 4 of {7}*14
10 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2, ((s1*s0)^2*s1*s2)^2> of order 16
4 facets
- 4 of {7}*14
10 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2> of order 16
4 facets
- 4 of {7}*14
9 vertex figures
P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2, (s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 16
4 facets
- 4 of {7}*14
11 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*s2*(s1*s0)^2*s2, ((s1*s0)^2*s1*s2)^2> of order 16
4 facets
- 4 of {7}*14
7 vertex figures
- 7 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0*s1*s2)^2, (s0*s1)^2*s2*(s1*s0)^2*s2, (s1*s0)^2*s1*s2*(s1*s0)^2*s2*s1*s2> of order 16
4 facets
- 4 of {7}*14
10 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 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);; s1 := ( 2,33)( 3,25)( 4,57)( 5,49)( 6,17)( 7,41)( 8, 9)(10,40)(11,32)(12,64)(13,56)(14,24)(15,48)(18,38)(19,30)(20,62)(21,54)(23,46)(26,35)(28,59)(29,51)(31,43)(36,58)(37,50)(39,42)(44,63)(45,55)(52,61);; s2 := ( 1,19)( 2,20)( 3,17)( 4,18)( 5,23)( 6,24)( 7,21)( 8,22)( 9,27)(10,28)(11,25)(12,26)(13,31)(14,32)(15,29)(16,30)(33,51)(34,52)(35,49)(36,50)(37,55)(38,56)(39,53)(40,54)(41,59)(42,60)(43,57)(44,58)(45,63)(46,64)(47,61)(48,62);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)!( 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); s1 := Sym(64)!( 2,33)( 3,25)( 4,57)( 5,49)( 6,17)( 7,41)( 8, 9)(10,40)(11,32)(12,64)(13,56)(14,24)(15,48)(18,38)(19,30)(20,62)(21,54)(23,46)(26,35)(28,59)(29,51)(31,43)(36,58)(37,50)(39,42)(44,63)(45,55)(52,61); s2 := Sym(64)!( 1,19)( 2,20)( 3,17)( 4,18)( 5,23)( 6,24)( 7,21)( 8,22)( 9,27)(10,28)(11,25)(12,26)(13,31)(14,32)(15,29)(16,30)(33,51)(34,52)(35,49)(36,50)(37,55)(38,56)(39,53)(40,54)(41,59)(42,60)(43,57)(44,58)(45,63)(46,64)(47,61)(48,62); 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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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.