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