Overview
- Group
- SmallGroup(1440,5685)
- Rank
- 5
- Schläfli Type
- {3,2,30,4}
- Vertices, edges, …
- 3, 3, 30, 60, 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
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 := ( 5, 8)( 6, 7)( 9,14)(10,18)(11,17)(12,16)(13,15)(20,23)(21,22)(24,29)(25,33)(26,32)(27,31)(28,30)(35,38)(36,37)(39,44)(40,48)(41,47)(42,46)(43,45)(50,53)(51,52)(54,59)(55,63)(56,62)(57,61)(58,60);; s3 := ( 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)(34,55)(35,54)(36,58)(37,57)(38,56)(39,50)(40,49)(41,53)(42,52)(43,51)(44,60)(45,59)(46,63)(47,62)(48,61);; s4 := ( 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)(33,63);; 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*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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(63)!(2,3); s1 := Sym(63)!(1,2); s2 := Sym(63)!( 5, 8)( 6, 7)( 9,14)(10,18)(11,17)(12,16)(13,15)(20,23)(21,22)(24,29)(25,33)(26,32)(27,31)(28,30)(35,38)(36,37)(39,44)(40,48)(41,47)(42,46)(43,45)(50,53)(51,52)(54,59)(55,63)(56,62)(57,61)(58,60); s3 := 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)(34,55)(35,54)(36,58)(37,57)(38,56)(39,50)(40,49)(41,53)(42,52)(43,51)(44,60)(45,59)(46,63)(47,62)(48,61); s4 := Sym(63)!( 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)(33,63); 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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;