Overview
- Group
- SmallGroup(1440,5900)
- Rank
- 4
- Schläfli Type
- {2,15,12}
- Vertices, edges, …
- 2, 30, 180, 24
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
5-fold
6-fold
12-fold
15-fold
20-fold
30-fold
36-fold
60-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(23,43)(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)(34,58)(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50);; s2 := ( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)(12,42)(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)(43,47)(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58);; s3 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,46)(24,45)(25,44)(26,43)(27,50)(28,49)(29,48)(30,47)(31,54)(32,53)(33,52)(34,51)(35,58)(36,57)(37,56)(38,55)(39,62)(40,61)(41,60)(42,59);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s1,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(62)!(1,2); s1 := Sym(62)!( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(23,43)(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)(34,58)(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50); s2 := Sym(62)!( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)(12,42)(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)(43,47)(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58); s3 := Sym(62)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,14)(12,13)(15,18)(16,17)(19,22)(20,21)(23,46)(24,45)(25,44)(26,43)(27,50)(28,49)(29,48)(30,47)(31,54)(32,53)(33,52)(34,51)(35,58)(36,57)(37,56)(38,55)(39,62)(40,61)(41,60)(42,59); poly := sub<Sym(62)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s1*s3*s2*s3*s1, s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;