Overview
- Group
- SmallGroup(1920,240996)
- Rank
- 3
- Schläfli Type
- {8,5}
- Vertices, edges, …
- 192, 480, 120
- Order of s0s1s2
- 12
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
16-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)^2*s2*(s1*s0)^3*s1*s2*s1*s0*s1> of order 2
72 facets
96 vertex figures
- 96 of {5}*10
P/N, where N=<s0*s1*s2*s1*s0*s2*(s1*s0)^3*(s2*s1)^2> of order 2
60 facets
- 60 of {8}*16
96 vertex figures
- 96 of {5}*10
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, (s0*s1)^2*(s2*(s1*s0)^2)^2*s2> of order 4
30 facets
- 30 of {8}*16
48 vertex figures
- 48 of {5}*10
P/N, where N=<s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 4
30 facets
- 30 of {8}*16
48 vertex figures
- 48 of {5}*10
P/N, where N=<s0*s1*s2*s1*s0*s2*(s1*s0)^3*(s2*s1)^2, ((s1*s0)^3*s1*s2)^2> of order 4
30 facets
- 30 of {8}*16
48 vertex figures
- 48 of {5}*10
P/N, where N=<((s1*s0)^3*s1*s2)^2, (s1*s0)^2*s2*(s1*s0)^3*s1*s2*s1*s0*s1> of order 4
36 facets
48 vertex figures
- 48 of {5}*10
P/N, where N=<s0*s1*s0*(s2*s1*s0*s1)^2*s2*s1, s0*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1, s1*s0*s1*s2*(s1*s0)^2*s2*s1*s0*s1*s2> of order 8
18 facets
24 vertex figures
- 24 of {5}*10
P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^3*s1*s2, s1*s2*(s1*s0)^2*s2*s1*s0*(s1*s2)^2> of order 8
21 facets
24 vertex figures
- 24 of {5}*10
P/N, where N=<(s0*s1)^4, s0*s2*(s1*s0)^3*s1*s2, s1*s0*s2*(s1*s0)^3*s1*s2*s1> of order 8
24 facets
24 vertex figures
- 24 of {5}*10
P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s1*s0*s2, (s1*s0)^2*(s2*s1*s0*s1)^2> of order 8
21 facets
24 vertex figures
- 24 of {5}*10
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5,10)( 6, 7)( 8, 9);; s1 := ( 1, 2)( 3, 5)( 4, 6)( 7,10);; s2 := ( 2, 7)( 3, 6)( 5, 8)( 9,10);; 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*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(10)!( 2, 3)( 5,10)( 6, 7)( 8, 9); s1 := Sym(10)!( 1, 2)( 3, 5)( 4, 6)( 7,10); s2 := Sym(10)!( 2, 7)( 3, 6)( 5, 8)( 9,10); poly := sub<Sym(10)|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*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1 >;
References
None.
to this polytope.