Overview
- Group
- SmallGroup(960,11332)
- Rank
- 5
- Schläfli Type
- {2,30,4,2}
- Vertices, edges, …
- 2, 30, 60, 4, 2
- 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
4-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 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59);; s2 := ( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,24)(19,23)(20,27)(21,26)(22,25)(28,29)(30,32)(33,54)(34,53)(35,57)(36,56)(37,55)(38,49)(39,48)(40,52)(41,51)(42,50)(43,59)(44,58)(45,62)(46,61)(47,60);; s3 := ( 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);; s4 := (63,64);; 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,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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*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(64)!(1,2); s1 := Sym(64)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(19,22)(20,21)(23,28)(24,32)(25,31)(26,30)(27,29)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59); s2 := Sym(64)!( 3, 9)( 4, 8)( 5,12)( 6,11)( 7,10)(13,14)(15,17)(18,24)(19,23)(20,27)(21,26)(22,25)(28,29)(30,32)(33,54)(34,53)(35,57)(36,56)(37,55)(38,49)(39,48)(40,52)(41,51)(42,50)(43,59)(44,58)(45,62)(46,61)(47,60); s3 := Sym(64)!( 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); s4 := Sym(64)!(63,64); poly := sub<Sym(64)|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, s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;