Overview
- Group
- SmallGroup(960,11219)
- Rank
- 5
- Schläfli Type
- {2,6,10,4}
- Vertices, edges, …
- 2, 6, 30, 20, 4
- Order of s0s1s2s3s4
- 60
- Order of s0s1s2s3s4s3s2s1
- 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
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62);; s2 := ( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)(20,26)(21,25)(22,24)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(44,47)(45,46)(48,53)(49,57)(50,56)(51,55)(52,54)(59,62)(60,61);; s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,49)(34,48)(35,52)(36,51)(37,50)(38,54)(39,53)(40,57)(41,56)(42,55)(43,59)(44,58)(45,62)(46,61)(47,60);; s4 := ( 3,33)( 4,34)( 5,35)( 6,36)( 7,37)( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(32,62);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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(62)!(1,2); s1 := Sym(62)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)(38,43)(39,44)(40,45)(41,46)(42,47)(53,58)(54,59)(55,60)(56,61)(57,62); s2 := Sym(62)!( 3, 8)( 4,12)( 5,11)( 6,10)( 7, 9)(14,17)(15,16)(18,23)(19,27)(20,26)(21,25)(22,24)(29,32)(30,31)(33,38)(34,42)(35,41)(36,40)(37,39)(44,47)(45,46)(48,53)(49,57)(50,56)(51,55)(52,54)(59,62)(60,61); s3 := Sym(62)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)(28,29)(30,32)(33,49)(34,48)(35,52)(36,51)(37,50)(38,54)(39,53)(40,57)(41,56)(42,55)(43,59)(44,58)(45,62)(46,61)(47,60); s4 := Sym(62)!( 3,33)( 4,34)( 5,35)( 6,36)( 7,37)( 8,38)( 9,39)(10,40)(11,41)(12,42)(13,43)(14,44)(15,45)(16,46)(17,47)(18,48)(19,49)(20,50)(21,51)(22,52)(23,53)(24,54)(25,55)(26,56)(27,57)(28,58)(29,59)(30,60)(31,61)(32,62); poly := sub<Sym(62)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;