Overview
- Group
- SmallGroup(1440,5282)
- Rank
- 5
- Schläfli Type
- {3,2,12,10}
- Vertices, edges, …
- 3, 3, 12, 60, 10
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 9,14)(10,15)(11,16)(12,17)(13,18)(24,29)(25,30)(26,31)(27,32)(28,33)(34,49)(35,50)(36,51)(37,52)(38,53)(39,59)(40,60)(41,61)(42,62)(43,63)(44,54)(45,55)(46,56)(47,57)(48,58);; s3 := ( 4,39)( 5,43)( 6,42)( 7,41)( 8,40)( 9,34)(10,38)(11,37)(12,36)(13,35)(14,44)(15,48)(16,47)(17,46)(18,45)(19,54)(20,58)(21,57)(22,56)(23,55)(24,49)(25,53)(26,52)(27,51)(28,50)(29,59)(30,63)(31,62)(32,61)(33,60);; s4 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43)(44,45)(46,48)(49,50)(51,53)(54,55)(56,58)(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*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,
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)!( 9,14)(10,15)(11,16)(12,17)(13,18)(24,29)(25,30)(26,31)(27,32)(28,33)(34,49)(35,50)(36,51)(37,52)(38,53)(39,59)(40,60)(41,61)(42,62)(43,63)(44,54)(45,55)(46,56)(47,57)(48,58); s3 := Sym(63)!( 4,39)( 5,43)( 6,42)( 7,41)( 8,40)( 9,34)(10,38)(11,37)(12,36)(13,35)(14,44)(15,48)(16,47)(17,46)(18,45)(19,54)(20,58)(21,57)(22,56)(23,55)(24,49)(25,53)(26,52)(27,51)(28,50)(29,59)(30,63)(31,62)(32,61)(33,60); s4 := Sym(63)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43)(44,45)(46,48)(49,50)(51,53)(54,55)(56,58)(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*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;