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