Overview
- Group
- SmallGroup(1152,157853)
- Rank
- 3
- Schläfli Type
- {4,9}
- Vertices, edges, …
- 64, 288, 144
- Order of s0s1s2
- 9
- 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
None in this atlas.
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)^2*s1*s0*(s1*s2)^4*s1> of order 2
72 facets
- 72 of {4}*8
32 vertex figures
- 32 of {9}*18
P/N, where N=<s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 2
72 facets
- 72 of {4}*8
32 vertex figures
- 32 of {9}*18
P/N, where N=<(s0*s2*s1)^3*s0*(s1*s2)^3> of order 2
72 facets
- 72 of {4}*8
32 vertex figures
- 32 of {9}*18
P/N, where N=<s0*(s2*s1)^2*(s0*s2*s1)^2*s0*(s1*s2)^4> of order 2
72 facets
- 72 of {4}*8
32 vertex figures
- 32 of {9}*18
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 2
72 facets
- 72 of {4}*8
32 vertex figures
- 32 of {9}*18
P/N, where N=<(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
44 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s1)^2, (s2*s1*s0)^2*(s1*s2)^2> of order 4
44 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s2*s1*s0)^3*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2> of order 4
48 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
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
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
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
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
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
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^3*(s1*s2)^3*s1> of order 4
40 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s1*s0*s1*s2)^2, s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^3*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1*s0*s1*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 4
44 facets
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*(s2*s1*s0)^3*(s1*s2)^3*s1> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^4> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
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
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1, s1*s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
36 facets
- 36 of {4}*8
16 vertex figures
- 16 of {9}*18
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
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
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
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
24 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
26 facets
8 vertex figures
- 8 of {9}*18
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
20 facets
8 vertex figures
- 8 of {9}*18
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
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
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*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
24 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s1*s0*s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
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
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s2*s1*s0)^3*(s1*s2)^3> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s0*(s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*(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
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3*s1> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s2*s1*s0*s1*s2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^3*s1> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
22 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s1)^2, (s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^4, s1*(s0*(s2*s1)^2)^2*s0*(s2*s1)^2> of order 8
20 facets
8 vertex figures
- 8 of {9}*18
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s1*s2*s1*s0*(s1*s2)^4> of order 8
18 facets
- 18 of {4}*8
8 vertex figures
- 8 of {9}*18
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*s2*s1*s0*s1*s2, (s2*s1*s0)^2*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 16
12 facets
4 vertex figures
- 4 of {9}*18
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 16
11 facets
4 vertex figures
- 4 of {9}*18
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
14 facets
4 vertex figures
- 4 of {9}*18
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s2*s1)^2*s0*s2*s1*s0*(s1*s2)^3> of order 16
15 facets
4 vertex figures
- 4 of {9}*18
Representations
Permutation Representation (GAP)
s0 := ( 1,33)( 2,34)( 3,35)( 4,36)( 5,37)( 6,38)( 7,39)( 8,40)( 9,41)(10,42)(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,49)(18,50)(19,51)(20,52)(21,53)(22,54)(23,55)(24,56)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)(32,64);; s1 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60);; s2 := ( 2, 9)( 3,13)( 4, 5)( 6,12)( 7,16)(11,14)(17,49)(18,57)(19,61)(20,53)(21,52)(22,60)(23,64)(24,56)(25,50)(26,58)(27,62)(28,54)(29,51)(30,59)(31,63)(32,55)(34,41)(35,45)(36,37)(38,44)(39,48)(43,46);; 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,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!( 1,33)( 2,34)( 3,35)( 4,36)( 5,37)( 6,38)( 7,39)( 8,40)( 9,41)(10,42)(11,43)(12,44)(13,45)(14,46)(15,47)(16,48)(17,49)(18,50)(19,51)(20,52)(21,53)(22,54)(23,55)(24,56)(25,57)(26,58)(27,59)(28,60)(29,61)(30,62)(31,63)(32,64); s1 := Sym(64)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,49)(10,50)(11,52)(12,51)(13,33)(14,34)(15,36)(16,35)(23,24)(25,53)(26,54)(27,56)(28,55)(29,37)(30,38)(31,40)(32,39)(41,61)(42,62)(43,64)(44,63)(47,48)(59,60); s2 := Sym(64)!( 2, 9)( 3,13)( 4, 5)( 6,12)( 7,16)(11,14)(17,49)(18,57)(19,61)(20,53)(21,52)(22,60)(23,64)(24,56)(25,50)(26,58)(27,62)(28,54)(29,51)(30,59)(31,63)(32,55)(34,41)(35,45)(36,37)(38,44)(39,48)(43,46); 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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.