Overview
- Group
- SmallGroup(1440,5282)
- Rank
- 5
- Schläfli Type
- {3,2,10,12}
- Vertices, edges, …
- 3, 3, 10, 60, 12
- 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 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62);; s3 := ( 4, 5)( 6, 8)( 9,15)(10,14)(11,18)(12,17)(13,16)(19,20)(21,23)(24,30)(25,29)(26,33)(27,32)(28,31)(34,50)(35,49)(36,53)(37,52)(38,51)(39,60)(40,59)(41,63)(42,62)(43,61)(44,55)(45,54)(46,58)(47,57)(48,56);; s4 := ( 4,39)( 5,40)( 6,41)( 7,42)( 8,43)( 9,34)(10,35)(11,36)(12,37)(13,38)(14,44)(15,45)(16,46)(17,47)(18,48)(19,54)(20,55)(21,56)(22,57)(23,58)(24,49)(25,50)(26,51)(27,52)(28,53)(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,
s2*s3*s2*s3*s2*s3*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!(2,3); s1 := Sym(63)!(1,2); s2 := Sym(63)!( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(45,48)(46,47)(50,53)(51,52)(55,58)(56,57)(60,63)(61,62); s3 := Sym(63)!( 4, 5)( 6, 8)( 9,15)(10,14)(11,18)(12,17)(13,16)(19,20)(21,23)(24,30)(25,29)(26,33)(27,32)(28,31)(34,50)(35,49)(36,53)(37,52)(38,51)(39,60)(40,59)(41,63)(42,62)(43,61)(44,55)(45,54)(46,58)(47,57)(48,56); s4 := Sym(63)!( 4,39)( 5,40)( 6,41)( 7,42)( 8,43)( 9,34)(10,35)(11,36)(12,37)(13,38)(14,44)(15,45)(16,46)(17,47)(18,48)(19,54)(20,55)(21,56)(22,57)(23,58)(24,49)(25,50)(26,51)(27,52)(28,53)(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, s2*s3*s2*s3*s2*s3*s2*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 >;