Overview
- Group
- SmallGroup(1440,5871)
- Rank
- 4
- Schläfli Type
- {6,6,15}
- Vertices, edges, …
- 6, 24, 60, 20
- Order of s0s1s2s3
- 60
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
12-fold
15-fold
24-fold
30-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60);; s1 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)(47,48)(51,52)(55,56)(59,60);; s2 := ( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(22,24)(25,37)(26,40)(27,39)(28,38)(29,33)(30,36)(31,35)(32,34)(42,44)(45,57)(46,60)(47,59)(48,58)(49,53)(50,56)(51,55)(52,54);; s3 := ( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14)(21,26)(22,25)(23,27)(24,28)(29,38)(30,37)(31,39)(32,40)(33,34)(41,46)(42,45)(43,47)(44,48)(49,58)(50,57)(51,59)(52,60)(53,54);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(60)!(21,41)(22,42)(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60); s1 := Sym(60)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,25)( 6,26)( 7,28)( 8,27)( 9,29)(10,30)(11,32)(12,31)(13,33)(14,34)(15,36)(16,35)(17,37)(18,38)(19,40)(20,39)(43,44)(47,48)(51,52)(55,56)(59,60); s2 := Sym(60)!( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(22,24)(25,37)(26,40)(27,39)(28,38)(29,33)(30,36)(31,35)(32,34)(42,44)(45,57)(46,60)(47,59)(48,58)(49,53)(50,56)(51,55)(52,54); s3 := Sym(60)!( 1, 6)( 2, 5)( 3, 7)( 4, 8)( 9,18)(10,17)(11,19)(12,20)(13,14)(21,26)(22,25)(23,27)(24,28)(29,38)(30,37)(31,39)(32,40)(33,34)(41,46)(42,45)(43,47)(44,48)(49,58)(50,57)(51,59)(52,60)(53,54); poly := sub<Sym(60)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3 >;
References
None.
to this polytope.