Overview
- Group
- SmallGroup(960,11209)
- Rank
- 5
- Schläfli Type
- {2,2,6,20}
- Vertices, edges, …
- 2, 2, 6, 60, 20
- 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 := (3,4);; s2 := (10,15)(11,16)(12,17)(13,18)(14,19)(25,30)(26,31)(27,32)(28,33)(29,34)(40,45)(41,46)(42,47)(43,48)(44,49)(55,60)(56,61)(57,62)(58,63)(59,64);; s3 := ( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(16,19)(17,18)(20,25)(21,29)(22,28)(23,27)(24,26)(31,34)(32,33)(35,55)(36,59)(37,58)(38,57)(39,56)(40,50)(41,54)(42,53)(43,52)(44,51)(45,60)(46,64)(47,63)(48,62)(49,61);; s4 := ( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,41)(11,40)(12,44)(13,43)(14,42)(15,46)(16,45)(17,49)(18,48)(19,47)(20,51)(21,50)(22,54)(23,53)(24,52)(25,56)(26,55)(27,59)(28,58)(29,57)(30,61)(31,60)(32,64)(33,63)(34,62);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!(1,2); s1 := Sym(64)!(3,4); s2 := Sym(64)!(10,15)(11,16)(12,17)(13,18)(14,19)(25,30)(26,31)(27,32)(28,33)(29,34)(40,45)(41,46)(42,47)(43,48)(44,49)(55,60)(56,61)(57,62)(58,63)(59,64); s3 := Sym(64)!( 5,10)( 6,14)( 7,13)( 8,12)( 9,11)(16,19)(17,18)(20,25)(21,29)(22,28)(23,27)(24,26)(31,34)(32,33)(35,55)(36,59)(37,58)(38,57)(39,56)(40,50)(41,54)(42,53)(43,52)(44,51)(45,60)(46,64)(47,63)(48,62)(49,61); s4 := Sym(64)!( 5,36)( 6,35)( 7,39)( 8,38)( 9,37)(10,41)(11,40)(12,44)(13,43)(14,42)(15,46)(16,45)(17,49)(18,48)(19,47)(20,51)(21,50)(22,54)(23,53)(24,52)(25,56)(26,55)(27,59)(28,58)(29,57)(30,61)(31,60)(32,64)(33,63)(34,62); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;