Overview
- Group
- SmallGroup(1440,5685)
- Rank
- 5
- Schläfli Type
- {3,2,4,30}
- Vertices, edges, …
- 3, 3, 4, 60, 30
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := (34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63);; s3 := ( 4,34)( 5,38)( 6,37)( 7,36)( 8,35)( 9,44)(10,48)(11,47)(12,46)(13,45)(14,39)(15,43)(16,42)(17,41)(18,40)(19,49)(20,53)(21,52)(22,51)(23,50)(24,59)(25,63)(26,62)(27,61)(28,60)(29,54)(30,58)(31,57)(32,56)(33,55);; s4 := ( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,25)(20,24)(21,28)(22,27)(23,26)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48)(49,55)(50,54)(51,58)(52,57)(53,56)(59,60)(61,63);; 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*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,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*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*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(63)!(2,3); s1 := Sym(63)!(1,2); s2 := Sym(63)!(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60)(46,61)(47,62)(48,63); s3 := Sym(63)!( 4,34)( 5,38)( 6,37)( 7,36)( 8,35)( 9,44)(10,48)(11,47)(12,46)(13,45)(14,39)(15,43)(16,42)(17,41)(18,40)(19,49)(20,53)(21,52)(22,51)(23,50)(24,59)(25,63)(26,62)(27,61)(28,60)(29,54)(30,58)(31,57)(32,56)(33,55); s4 := Sym(63)!( 4,10)( 5, 9)( 6,13)( 7,12)( 8,11)(14,15)(16,18)(19,25)(20,24)(21,28)(22,27)(23,26)(29,30)(31,33)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48)(49,55)(50,54)(51,58)(52,57)(53,56)(59,60)(61,63); poly := sub<Sym(63)|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*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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;