Overview
- Group
- SmallGroup(480,1088)
- Rank
- 4
- Schläfli Type
- {6,20,2}
- Vertices, edges, …
- 6, 60, 20, 2
- Order of s0s1s2s3
- 60
- 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
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
Representations
Permutation Representation (GAP)
s0 := ( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60);; s1 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,51)(32,55)(33,54)(34,53)(35,52)(36,46)(37,50)(38,49)(39,48)(40,47)(41,56)(42,60)(43,59)(44,58)(45,57);; s2 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,37)( 7,36)( 8,40)( 9,39)(10,38)(11,42)(12,41)(13,45)(14,44)(15,43)(16,47)(17,46)(18,50)(19,49)(20,48)(21,52)(22,51)(23,55)(24,54)(25,53)(26,57)(27,56)(28,60)(29,59)(30,58);; s3 := (61,62);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!( 6,11)( 7,12)( 8,13)( 9,14)(10,15)(21,26)(22,27)(23,28)(24,29)(25,30)(36,41)(37,42)(38,43)(39,44)(40,45)(51,56)(52,57)(53,58)(54,59)(55,60); s1 := Sym(62)!( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,51)(32,55)(33,54)(34,53)(35,52)(36,46)(37,50)(38,49)(39,48)(40,47)(41,56)(42,60)(43,59)(44,58)(45,57); s2 := Sym(62)!( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,37)( 7,36)( 8,40)( 9,39)(10,38)(11,42)(12,41)(13,45)(14,44)(15,43)(16,47)(17,46)(18,50)(19,49)(20,48)(21,52)(22,51)(23,55)(24,54)(25,53)(26,57)(27,56)(28,60)(29,59)(30,58); s3 := Sym(62)!(61,62); poly := sub<Sym(62)|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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;