Overview
- Group
- SmallGroup(480,1087)
- Rank
- 5
- Schläfli Type
- {12,2,5,2}
- Vertices, edges, …
- 12, 12, 5, 5, 2
- Order of s0s1s2s3s4
- 60
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);; s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);; s2 := (14,15)(16,17);; s3 := (13,14)(15,16);; s4 := (18,19);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(19)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12); s1 := Sym(19)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12); s2 := Sym(19)!(14,15)(16,17); s3 := Sym(19)!(13,14)(15,16); s4 := Sym(19)!(18,19); poly := sub<Sym(19)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;