Overview
- Group
- SmallGroup(600,195)
- Rank
- 4
- Schläfli Type
- {5,2,30}
- Vertices, edges, …
- 5, 5, 30, 30
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 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
5-fold
6-fold
10-fold
15-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (2,3)(4,5);; s1 := (1,2)(3,4);; s2 := ( 8, 9)(10,11)(12,13)(14,15)(16,19)(17,18)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,35)(33,34);; s3 := ( 6,22)( 7,16)( 8,14)( 9,24)(10,12)(11,32)(13,18)(15,28)(17,26)(19,34)(20,23)(21,33)(25,30)(27,29)(31,35);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(35)!(2,3)(4,5); s1 := Sym(35)!(1,2)(3,4); s2 := Sym(35)!( 8, 9)(10,11)(12,13)(14,15)(16,19)(17,18)(20,21)(22,25)(23,24)(26,27)(28,31)(29,30)(32,35)(33,34); s3 := Sym(35)!( 6,22)( 7,16)( 8,14)( 9,24)(10,12)(11,32)(13,18)(15,28)(17,26)(19,34)(20,23)(21,33)(25,30)(27,29)(31,35); poly := sub<Sym(35)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;