Overview
- Group
- SmallGroup(1320,133)
- Rank
- 3
- Schläfli Type
- {4,10}
- Vertices, edges, …
- 66, 330, 165
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 5
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7, 9);; s1 := ( 1, 2)( 3, 5)( 4, 6)( 7,10)( 8,11)( 9,12);; s2 := ( 1, 2)( 3, 6)( 4, 7)( 8, 9)(10,12);; 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,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!( 1, 3)( 2, 6)( 4, 8)( 5,11)( 7, 9); s1 := Sym(12)!( 1, 2)( 3, 5)( 4, 6)( 7,10)( 8,11)( 9,12); s2 := Sym(12)!( 1, 2)( 3, 6)( 4, 7)( 8, 9)(10,12); 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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.