Overview
- Group
- SmallGroup(1440,5843)
- Rank
- 4
- Schläfli Type
- {2,10,10}
- Vertices, edges, …
- 2, 36, 180, 36
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
No regular quotients.
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4,10)( 5, 7)( 6, 9)( 8,11);; s2 := ( 3, 4)( 5, 6)( 7,11)( 8,10)( 9,12);; s3 := ( 3,12)( 4, 8)( 6, 9)(10,11);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3,
s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(12)!(1,2); s1 := Sym(12)!( 4,10)( 5, 7)( 6, 9)( 8,11); s2 := Sym(12)!( 3, 4)( 5, 6)( 7,11)( 8,10)( 9,12); s3 := Sym(12)!( 3,12)( 4, 8)( 6, 9)(10,11); poly := sub<Sym(12)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3, s1*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2 >;