Overview
- Group
- SmallGroup(960,10886)
- Rank
- 5
- Schläfli Type
- {5,6,2,4}
- Vertices, edges, …
- 10, 30, 12, 4, 4
- Order of s0s1s2s3s4
- 20
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
Covers minimal covers in bold
2-fold
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);; s3 := (14,15);; s4 := (13,14)(15,16);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4*s3*s4, 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(16)!( 1, 3)( 2, 8)( 4,12)( 5, 7)( 6, 9)(10,11); s1 := Sym(16)!( 1, 4)( 2, 7)( 3,11)( 5,10)( 6, 9)( 8,12); s2 := Sym(16)!( 1, 3)( 2, 6)( 8, 9)(10,11); s3 := Sym(16)!(14,15); s4 := Sym(16)!(13,14)(15,16); poly := sub<Sym(16)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 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 >;