Overview
- Group
- SmallGroup(120,35)
- Rank
- 3
- Schläfli Type
- {5,5}
- Vertices, edges, …
- 12, 30, 12
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 3
- Also known as
- {5,5|3}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
Covers minimal covers in bold
2-fold
4-fold
5-fold
6-fold
8-fold
10-fold
12-fold
14-fold
16-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 9)( 4,12)( 5, 7)( 6, 8);; s1 := ( 3, 5)( 4,11)( 6,12)( 7, 9);; s2 := ( 1,11)( 3,10)( 4, 7)( 5,12);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 2, 9)( 4,12)( 5, 7)( 6, 8); s1 := Sym(12)!( 3, 5)( 4,11)( 6,12)( 7, 9); s2 := Sym(12)!( 1,11)( 3,10)( 4, 7)( 5,12); poly := sub<Sym(12)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.