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