Overview
- Group
- SmallGroup(1440,5871)
- Rank
- 4
- Schläfli Type
- {15,6,6}
- Vertices, edges, …
- 20, 60, 24, 6
- 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 := ( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,13)(10,14)(11,16)(12,15)(23,24)(25,37)(26,38)(27,40)(28,39)(29,33)(30,34)(31,36)(32,35)(43,44)(45,57)(46,58)(47,60)(48,59)(49,53)(50,54)(51,56)(52,55);; s1 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56);; s2 := ( 1, 2)( 5, 6)( 9,10)(13,14)(17,18)(21,42)(22,41)(23,43)(24,44)(25,46)(26,45)(27,47)(28,48)(29,50)(30,49)(31,51)(32,52)(33,54)(34,53)(35,55)(36,56)(37,58)(38,57)(39,59)(40,60);; s3 := ( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40);; 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, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(60)!( 3, 4)( 5,17)( 6,18)( 7,20)( 8,19)( 9,13)(10,14)(11,16)(12,15)(23,24)(25,37)(26,38)(27,40)(28,39)(29,33)(30,34)(31,36)(32,35)(43,44)(45,57)(46,58)(47,60)(48,59)(49,53)(50,54)(51,56)(52,55); s1 := Sym(60)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,25)(22,28)(23,27)(24,26)(29,37)(30,40)(31,39)(32,38)(34,36)(41,45)(42,48)(43,47)(44,46)(49,57)(50,60)(51,59)(52,58)(54,56); s2 := Sym(60)!( 1, 2)( 5, 6)( 9,10)(13,14)(17,18)(21,42)(22,41)(23,43)(24,44)(25,46)(26,45)(27,47)(28,48)(29,50)(30,49)(31,51)(32,52)(33,54)(34,53)(35,55)(36,56)(37,58)(38,57)(39,59)(40,60); s3 := Sym(60)!( 1,21)( 2,22)( 3,23)( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40); 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, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0 >;
References
None.
to this polytope.