Overview
- Group
- SmallGroup(1792,1083553)
- Rank
- 3
- Schläfli Type
- {7,14}
- Vertices, edges, …
- 64, 448, 128
- Order of s0s1s2
- 4
- Order of s0s1s2s1
- 14
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-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)^3*s2*s1*s0*(s1*s2)^2*s1> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s1*s2*s1> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<(s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<(s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<s1*s0*(s1*s2)^2*(s1*s0*s1*s2)^2> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<s1*s0*s1*s2*s1*s0*(s1*s2)^4> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<s1*s2*s1*s0*(s1*s2)^3*s1*s0*s1*s2> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2*s1> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 2
64 facets
- 64 of {7}*14
32 vertex figures
- 32 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s1*s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^3*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*(s1*s0)^2*s1*s2, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s0*s2*(s1*s0)^3*(s2*s1)^2*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*(s2*s1)^2*s0*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0, s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2*s1, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1, s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2*s1, (s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2*s1, s1*s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s0*s2*(s1*s0)^2*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1, s0*s2*(s1*s0)^3*s2*s1*s0*s1*s2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*(s2*s1*s0*s1)^2, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*s2*s1*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1*s0*s1, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*(s2*s1)^2*(s0*s1)^2*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2*s1, s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^2*(s1*s0)^2*s1*s2*s1*s0*s1, s0*s2*(s1*s0)^3*(s2*s1)^2*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*(s2*s1)^2*(s0*s1)^2*s2*s1, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s1*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1*s2*s1)^3*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^4*s1*s0*s1*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s1*s2)^3*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*(s1*s2)^2*s1)^2*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*(s1*s2)^2*s1)^2*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^2*(s1*s0*s1*s2)^2*s1, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^3*s1*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s1*s0*(s1*s2)^2*(s1*s0*s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s0*s2*(s1*s0)^3*(s2*s1)^2, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s1*s0*(s1*s2)^4*s1*s0*s1*s2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s1*s0)^3*s2*s1*s0*s1*s2*s1, s1*s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1, s1*s0*s1*s2*s1*s0*(s1*s2)^4> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^4*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*(s2*s1*s0*s1)^2, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2*s1*s0*s1*s2*s1, s1*s0*s1*s2*s1*s0*(s1*s2)^4> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^3*s1*s0*(s1*s2)^2*s1, s1*s0*(s1*s2)^2*(s1*s0*s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^3*s1*s0*(s1*s2)^2*s1, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s0*s1*s2*(s1*s0)^2*(s1*s2)^2*s1*s0*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s1*s2*s1*s0*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s1*s0*(s1*s2)^2*(s1*s0)^2*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s1*s2*s1, s0*s2*(s1*s0)^3*s2*(s1*s0)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^3> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*(s1*s2)^2*s1> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<s0*(s1*s2)^2*s1*s0*(s1*s2)^3*s1, (s1*s0)^2*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 4
32 facets
- 32 of {7}*14
16 vertex figures
- 16 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*(s1*s0)^2*s2*s1*s0*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^3*s0*(s2*s1)^2*s0*s1*s2, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1, s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^2*s0*s2*(s1*s0)^3*s2*s1, s0*s1*s2*(s1*s0)^2*(s1*s2)^3*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s0*(s2*s1)^2*s0*s1*s2, s0*s1*s2*s1*s0*(s1*s2)^2*(s1*s0)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1, (s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s0*s2*(s1*s0)^3*s2*s1*s0*s1*s2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^2*(s2*s1)^2*(s0*s1)^2*s2*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s1*s2*s1*s0*s1, s0*s1*s2*s1*s0*(s1*s2)^4*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<s0*s2*(s1*s0)^2*s2*s1*s0*s1, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, s0*(s1*s2*(s1*s0)^2)^2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^3*s0*s2*s1*s0*s1*s2*s1*s0, (s0*s1)^2*s0*(s2*s1)^2*s0*s1*s0*s2*s1, s0*s2*(s1*s0)^3*s2*s1*s0*s1*s2*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, (s0*s1)^3*s2*s1*s0*(s1*s2)^2*s1, (s0*(s1*s2)^2*s1)^2*s0*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s1*s2)^2*s1*s0*s1, s0*s1*s0*(s2*s1)^2*s0*s1*s0*s2*s1*s0*s1, s0*s1*s2*s1*s0*(s1*s2)^4*s1> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
P/N, where N=<(s0*s1)^2*(s2*s1)^3*s0*s1*s2*s1, s0*s1*s2*(s1*s0)^2*(s1*s2)^3*s1, (s1*s0)^2*s1*s2*s1*s0*(s1*s2)^3> of order 8
16 facets
- 16 of {7}*14
8 vertex figures
- 8 of {14}*28
Representations
Permutation Representation (GAP)
s0 := ( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)( 10, 34)( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 21, 99)( 22,100)( 23,115)( 24,116)( 25, 35)( 26, 36)( 27, 51)( 28, 52)( 29, 67)( 30, 68)( 31, 83)( 32, 84)( 37,105)( 38,106)( 39,121)( 40,122)( 43, 57)( 44, 58)( 45, 73)( 46, 74)( 47, 89)( 48, 90)( 53,107)( 54,108)( 55,123)( 56,124)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,109)( 70,110)( 71,125)( 72,126)( 79, 93)( 80, 94)( 85,111)( 86,112)( 87,127)( 88,128)(103,117)(104,118);; s1 := ( 3, 33)( 4, 34)( 5,113)( 6,114)( 7, 81)( 8, 82)( 9, 65)( 10, 66)( 11, 97)( 12, 98)( 13, 49)( 14, 50)( 15, 17)( 16, 18)( 19, 47)( 20, 48)( 21,127)( 22,128)( 23, 95)( 24, 96)( 25, 79)( 26, 80)( 27,111)( 28,112)( 29, 63)( 30, 64)( 37,115)( 38,116)( 39, 83)( 40, 84)( 41, 67)( 42, 68)( 43, 99)( 44,100)( 45, 51)( 46, 52)( 53,125)( 54,126)( 55, 93)( 56, 94)( 57, 77)( 58, 78)( 59,109)( 60,110)( 69,121)( 70,122)( 71, 89)( 72, 90)( 75,105)( 76,106)( 85,119)( 86,120)( 91,103)( 92,104)(101,123)(102,124);; s2 := ( 1, 20)( 2, 19)( 3, 4)( 5,116)( 6,115)( 7,100)( 8, 99)( 9, 52)( 10, 51)( 11, 36)( 12, 35)( 13, 84)( 14, 83)( 15, 68)( 16, 67)( 17, 18)( 21,114)( 22,113)( 23, 98)( 24, 97)( 25, 50)( 26, 49)( 27, 34)( 28, 33)( 29, 82)( 30, 81)( 31, 66)( 32, 65)( 37,124)( 38,123)( 39,108)( 40,107)( 41, 60)( 42, 59)( 43, 44)( 45, 92)( 46, 91)( 47, 76)( 48, 75)( 53,122)( 54,121)( 55,106)( 56,105)( 57, 58)( 61, 90)( 62, 89)( 63, 74)( 64, 73)( 69,128)( 70,127)( 71,112)( 72,111)( 77, 96)( 78, 95)( 79, 80)( 85,126)( 86,125)( 87,110)( 88,109)( 93, 94)(101,120)(102,119)(103,104)(117,118);; 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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)( 10, 34)( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 21, 99)( 22,100)( 23,115)( 24,116)( 25, 35)( 26, 36)( 27, 51)( 28, 52)( 29, 67)( 30, 68)( 31, 83)( 32, 84)( 37,105)( 38,106)( 39,121)( 40,122)( 43, 57)( 44, 58)( 45, 73)( 46, 74)( 47, 89)( 48, 90)( 53,107)( 54,108)( 55,123)( 56,124)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,109)( 70,110)( 71,125)( 72,126)( 79, 93)( 80, 94)( 85,111)( 86,112)( 87,127)( 88,128)(103,117)(104,118); s1 := Sym(128)!( 3, 33)( 4, 34)( 5,113)( 6,114)( 7, 81)( 8, 82)( 9, 65)( 10, 66)( 11, 97)( 12, 98)( 13, 49)( 14, 50)( 15, 17)( 16, 18)( 19, 47)( 20, 48)( 21,127)( 22,128)( 23, 95)( 24, 96)( 25, 79)( 26, 80)( 27,111)( 28,112)( 29, 63)( 30, 64)( 37,115)( 38,116)( 39, 83)( 40, 84)( 41, 67)( 42, 68)( 43, 99)( 44,100)( 45, 51)( 46, 52)( 53,125)( 54,126)( 55, 93)( 56, 94)( 57, 77)( 58, 78)( 59,109)( 60,110)( 69,121)( 70,122)( 71, 89)( 72, 90)( 75,105)( 76,106)( 85,119)( 86,120)( 91,103)( 92,104)(101,123)(102,124); s2 := Sym(128)!( 1, 20)( 2, 19)( 3, 4)( 5,116)( 6,115)( 7,100)( 8, 99)( 9, 52)( 10, 51)( 11, 36)( 12, 35)( 13, 84)( 14, 83)( 15, 68)( 16, 67)( 17, 18)( 21,114)( 22,113)( 23, 98)( 24, 97)( 25, 50)( 26, 49)( 27, 34)( 28, 33)( 29, 82)( 30, 81)( 31, 66)( 32, 65)( 37,124)( 38,123)( 39,108)( 40,107)( 41, 60)( 42, 59)( 43, 44)( 45, 92)( 46, 91)( 47, 76)( 48, 75)( 53,122)( 54,121)( 55,106)( 56,105)( 57, 58)( 61, 90)( 62, 89)( 63, 74)( 64, 73)( 69,128)( 70,127)( 71,112)( 72,111)( 77, 96)( 78, 95)( 79, 80)( 85,126)( 86,125)( 87,110)( 88,109)( 93, 94)(101,120)(102,119)(103,104)(117,118); 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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.