Overview
- Group
- SmallGroup(1280,1116442)
- Rank
- 3
- Schläfli Type
- {4,10}
- Vertices, edges, …
- 64, 320, 160
- Order of s0s1s2
- 20
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
64-fold
80-fold
160-fold
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*s2)^2*s1*s0*(s1*s2)^2*s1> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*(s1*s0*s2*s1*s0*(s1*s2)^2)^2> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^2> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s1*s2)^3> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 2
80 facets
- 80 of {4}*8
32 vertex figures
- 32 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^2, (s1*s0*s2)^4*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^3*s0*(s2*s1)^2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^2*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s2*s1)^2, s0*(s2*s1)^2*(s0*s2*s1)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s0*(s1*s2)^3*s1)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s2*s1*s0)^3*(s1*s2)^3, (s0*(s1*s2)^3*s1)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s2*s1*s0*(s2*s1)^2*s0*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2, (s1*s0*s2)^4*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s2*s1)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*(s2*s1)^2*s0*(s2*s1)^3, (s0*s2*s1)^2*s0*(s2*s1)^2*s0*s2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, (s1*s0*(s1*s2)^3)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s1*s0*(s1*s2)^3)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s2)^2*s1*s0*(s2*s1)^2*s0*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*s1*s2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s0*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2, s1*s0*s1*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s1*s2)^2, s0*(s2*s1)^4*s0*(s1*s2)^4> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*(s1*s2)^3*s1)^2, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2, s0*(s2*s1)^2*(s0*s2*s1)^3> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, s0*s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 4
56 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s1*s2)^3, s0*(s2*s1)^4*s0*(s1*s2)^4> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s2*s1*s0*s1*s2, (s1*s2)^5> of order 4
48 facets
24 vertex figures
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*(s2*s1)^2*s0*(s2*s1)^3, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s2*s1)^3*s0*(s1*s2)^3, s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s2)^5, s1*s0*(s2*s1)^3*s0*s2*s1*s2> of order 4
40 facets
- 40 of {4}*8
24 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s0*s1)^2*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 4
48 facets
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s2)^5, s0*s1*(s2*s1*s0)^3*s2*s1*s2> of order 4
40 facets
- 40 of {4}*8
24 vertex figures
P/N, where N=<(s1*s2)^5, (s0*s2*s1)^3*s0*(s2*s1)^2> of order 4
40 facets
- 40 of {4}*8
24 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s1*s2*s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 4
40 facets
- 40 of {4}*8
16 vertex figures
- 16 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s2*s1)^3, s0*(s1*s0*s2)^2*s1*s0*(s2*s1)^2*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*s1*s0*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^2*s0*s2*s1> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^3, s0*s1*s2*s1*s0*(s2*s1)^2*s0*s2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s0*s2*s1*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s1*s2)^2*s1*s0*(s2*s1)^2*s0*s1*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*(s1*s2)^2*s1)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^3, s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^3, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(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
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, (s2*s1*s0)^3*(s1*s2)^3> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
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)^2*s1*s0*s1*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s2*s1)^2*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
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> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*(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
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s1*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, s0*(s2*s1)^2*s0*(s2*s1)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s2*s1)^3*s2, s0*(s2*s1)^2*s0*(s2*s1)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s2*s1)^3, s0*(s2*s1)^3*s0*(s2*s1)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^3*s2, s0*(s2*s1)^2*s0*(s2*s1)^3, s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*(s2*s1)^2*s0*(s2*s1)^3, s0*(s2*s1)^3*s0*(s2*s1)^2, (s0*s2*s1)^2*s0*(s2*s1)^2*s0*s2*s1> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, (s1*s2)^5, (s0*s2*s1)^3*s0*(s2*s1)^2> of order 8
24 facets
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^5> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s2)^5, (s0*(s1*s2)^2*s1)^2> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<(s1*s2)^5, (s0*(s1*s2)^2*s1)^2, s1*s0*(s2*s1)^3*s0*s2*s1*s2> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<s0*s2*s1*s0*s1*s2, (s1*s2)^5, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
28 facets
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s2)^5, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
12 vertex figures
P/N, where N=<(s1*s2)^5, s1*s0*(s2*s1)^3*s0*s2*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
24 facets
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s2)^5, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<(s1*s2)^5, s1*s0*(s2*s1)^3*s0*s2*s1*s2, (s0*s2*s1)^3*s0*(s2*s1)^2> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s2)^5, s0*s1*(s2*s1*s0)^3*s2*s1*s2> of order 8
20 facets
- 20 of {4}*8
12 vertex figures
P/N, where N=<s0*(s2*s1)^2*s0*(s2*s1)^3, s1*s2*s1*s0*(s2*s1)^2*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1, s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s2*s1)^2*s2, s1*s2*s1*s0*(s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*(s2*s1)^3*s0*s2*s1*s0*s2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s2*s1)^2*s0*(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s0*(s1*s2)^2*s1)^2, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s0*(s1*s2)^2*s1)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s0*(s1*s2)^2*s1)^2, s0*(s2*s1)^3*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*(s1*s2)^2*s1)^2, s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s1*s2)^5> of order 8
24 facets
12 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
32 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, (s0*(s1*s2)^3*s1)^2, (s0*s2*s1)^3*s0*(s1*s2)^3> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*s0*(s1*s2)^2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s1*s2)^5> of order 8
28 facets
12 vertex figures
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 8
24 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1, (s0*(s1*s2)^3*s1)^2> of order 8
20 facets
- 20 of {4}*8
8 vertex figures
- 8 of {10}*20
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1, s1*s0*(s2*s1)^3*s0*(s1*s2)^3*s1> of order 8
28 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2> of order 8
32 facets
8 vertex figures
- 8 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, (s1*s2)^5> of order 16
16 facets
6 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s2*s1*s0)^2*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16
14 facets
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 16
18 facets
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16
14 facets
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 16
14 facets
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 16
10 facets
- 10 of {4}*8
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 16
10 facets
- 10 of {4}*8
4 vertex figures
- 4 of {10}*20
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s1*s2)^5, (s0*(s1*s2)^2*s1)^2> of order 16
12 facets
6 vertex figures
P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^5> of order 16
12 facets
6 vertex figures
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s1*s2)^5, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 16
16 facets
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 1, 61)( 2, 62)( 3, 64)( 4, 63)( 5, 57)( 6, 58)( 7, 60)( 8, 59)( 9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 49)( 14, 50)( 15, 52)( 16, 51)( 17, 45)( 18, 46)( 19, 48)( 20, 47)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)( 83,112)( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99);; s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 99)( 10,100)( 11, 97)( 12, 98)( 13,103)( 14,104)( 15,101)( 16,102)( 17, 59)( 18, 60)( 19, 57)( 20, 58)( 21, 63)( 22, 64)( 23, 61)( 24, 62)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 75)( 34, 76)( 35, 73)( 36, 74)( 37, 79)( 38, 80)( 39, 77)( 40, 78)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 81,123)( 82,124)( 83,121)( 84,122)( 85,127)( 86,128)( 87,125)( 88,126)(105,107)(106,108)(109,111)(110,112);; s2 := ( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112);; 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*s1*s2,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 1, 61)( 2, 62)( 3, 64)( 4, 63)( 5, 57)( 6, 58)( 7, 60)( 8, 59)( 9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 49)( 14, 50)( 15, 52)( 16, 51)( 17, 45)( 18, 46)( 19, 48)( 20, 47)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)( 83,112)( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99); s1 := Sym(128)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 99)( 10,100)( 11, 97)( 12, 98)( 13,103)( 14,104)( 15,101)( 16,102)( 17, 59)( 18, 60)( 19, 57)( 20, 58)( 21, 63)( 22, 64)( 23, 61)( 24, 62)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 75)( 34, 76)( 35, 73)( 36, 74)( 37, 79)( 38, 80)( 39, 77)( 40, 78)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 81,123)( 82,124)( 83,121)( 84,122)( 85,127)( 86,128)( 87,125)( 88,126)(105,107)(106,108)(109,111)(110,112); s2 := Sym(128)!( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112); poly := sub<Sym(128)|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*s1*s2, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.