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