Overview
- Group
- SmallGroup(1440,5900)
- Rank
- 4
- Schläfli Type
- {2,12,15}
- Vertices, edges, …
- 2, 24, 180, 30
- 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 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,45)(24,46)(25,43)(26,44)(27,49)(28,50)(29,47)(30,48)(31,53)(32,54)(33,51)(34,52)(35,57)(36,58)(37,55)(38,56)(39,61)(40,62)(41,59)(42,60);; s2 := ( 3,23)( 4,25)( 5,24)( 6,26)( 7,39)( 8,41)( 9,40)(10,42)(11,35)(12,37)(13,36)(14,38)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(44,45)(47,59)(48,61)(49,60)(50,62)(51,55)(52,57)(53,56)(54,58);; s3 := ( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,19)(12,22)(13,21)(14,20)(16,18)(23,47)(24,50)(25,49)(26,48)(27,43)(28,46)(29,45)(30,44)(31,59)(32,62)(33,61)(34,60)(35,55)(36,58)(37,57)(38,56)(39,51)(40,54)(41,53)(42,52);; 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1,
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(62)!(1,2); s1 := Sym(62)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)(23,45)(24,46)(25,43)(26,44)(27,49)(28,50)(29,47)(30,48)(31,53)(32,54)(33,51)(34,52)(35,57)(36,58)(37,55)(38,56)(39,61)(40,62)(41,59)(42,60); s2 := Sym(62)!( 3,23)( 4,25)( 5,24)( 6,26)( 7,39)( 8,41)( 9,40)(10,42)(11,35)(12,37)(13,36)(14,38)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(44,45)(47,59)(48,61)(49,60)(50,62)(51,55)(52,57)(53,56)(54,58); s3 := Sym(62)!( 3, 7)( 4,10)( 5, 9)( 6, 8)(11,19)(12,22)(13,21)(14,20)(16,18)(23,47)(24,50)(25,49)(26,48)(27,43)(28,46)(29,45)(30,44)(31,59)(32,62)(33,61)(34,60)(35,55)(36,58)(37,57)(38,56)(39,51)(40,54)(41,53)(42,52); 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1, 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 >;