Overview
- Group
- SmallGroup(960,11219)
- Rank
- 5
- Schläfli Type
- {10,6,4,2}
- Vertices, edges, …
- 10, 30, 12, 4, 2
- 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
2-fold
Representations
Permutation Representation (GAP)
s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59);; s1 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43)(46,47)(48,50)(51,57)(52,56)(53,60)(54,59)(55,58);; s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)(31,51)(32,52)(33,53)(34,54)(35,55)(36,46)(37,47)(38,48)(39,49)(40,50)(41,56)(42,57)(43,58)(44,59)(45,60);; s3 := ( 1,31)( 2,32)( 3,33)( 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);; s4 := (61,62);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)(53,54)(57,60)(58,59); s1 := Sym(62)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)(22,26)(23,30)(24,29)(25,28)(31,32)(33,35)(36,42)(37,41)(38,45)(39,44)(40,43)(46,47)(48,50)(51,57)(52,56)(53,60)(54,59)(55,58); s2 := Sym(62)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)(31,51)(32,52)(33,53)(34,54)(35,55)(36,46)(37,47)(38,48)(39,49)(40,50)(41,56)(42,57)(43,58)(44,59)(45,60); s3 := Sym(62)!( 1,31)( 2,32)( 3,33)( 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); s4 := Sym(62)!(61,62); poly := sub<Sym(62)|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, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;