Overview
- Group
- SmallGroup(240,190)
- Rank
- 4
- Schläfli Type
- {2,5,6}
- Vertices, edges, …
- 2, 10, 30, 12
- Order of s0s1s2s3
- 10
- 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
2-fold
Covers minimal covers in bold
2-fold
4-fold
6-fold
8-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 5)( 4,10)( 6,14)( 7, 9)( 8,11)(12,13);; s2 := ( 3, 6)( 4, 9)( 5,13)( 7,12)( 8,11)(10,14);; s3 := ( 3, 5)( 4, 8)(10,11)(12,13);; 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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(14)!(1,2); s1 := Sym(14)!( 3, 5)( 4,10)( 6,14)( 7, 9)( 8,11)(12,13); s2 := Sym(14)!( 3, 6)( 4, 9)( 5,13)( 7,12)( 8,11)(10,14); s3 := Sym(14)!( 3, 5)( 4, 8)(10,11)(12,13); poly := sub<Sym(14)|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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s1 >;