Overview
- Group
- SmallGroup(720,831)
- Rank
- 4
- Schläfli Type
- {6,2,30}
- Vertices, edges, …
- 6, 6, 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
4-fold
5-fold
6-fold
9-fold
10-fold
12-fold
15-fold
18-fold
20-fold
30-fold
45-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6);; s1 := (1,5)(2,3)(4,6);; s2 := ( 9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,28)(29,32)(30,31)(33,36)(34,35);; s3 := ( 7,23)( 8,17)( 9,15)(10,25)(11,13)(12,33)(14,19)(16,29)(18,27)(20,35)(21,24)(22,34)(26,31)(28,30)(32,36);; 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*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(36)!(3,4)(5,6); s1 := Sym(36)!(1,5)(2,3)(4,6); s2 := Sym(36)!( 9,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22)(23,26)(24,25)(27,28)(29,32)(30,31)(33,36)(34,35); s3 := Sym(36)!( 7,23)( 8,17)( 9,15)(10,25)(11,13)(12,33)(14,19)(16,29)(18,27)(20,35)(21,24)(22,34)(26,31)(28,30)(32,36); poly := sub<Sym(36)|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*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 >;