Overview
- Group
- SmallGroup(720,793)
- Rank
- 3
- Schläfli Type
- {30,12}
- Vertices, edges, …
- 30, 180, 12
- Order of s0s1s2
- 15
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
6-fold
15-fold
30-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)(22,23)(25,37)(26,39)(27,38)(28,40)(29,33)(30,35)(31,34)(32,36)(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56);; s1 := ( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,45)(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,57)(30,60)(31,59)(32,58)(33,53)(34,56)(35,55)(36,54)(37,49)(38,52)(39,51)(40,50);; s2 := ( 1,24)( 2,23)( 3,22)( 4,21)( 5,28)( 6,27)( 7,26)( 8,25)( 9,32)(10,31)(11,30)(12,29)(13,36)(14,35)(15,34)(16,33)(17,40)(18,39)(19,38)(20,37)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*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(60)!( 2, 3)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,15)(11,14)(12,16)(22,23)(25,37)(26,39)(27,38)(28,40)(29,33)(30,35)(31,34)(32,36)(42,43)(45,57)(46,59)(47,58)(48,60)(49,53)(50,55)(51,54)(52,56); s1 := Sym(60)!( 1, 5)( 2, 8)( 3, 7)( 4, 6)( 9,17)(10,20)(11,19)(12,18)(14,16)(21,45)(22,48)(23,47)(24,46)(25,41)(26,44)(27,43)(28,42)(29,57)(30,60)(31,59)(32,58)(33,53)(34,56)(35,55)(36,54)(37,49)(38,52)(39,51)(40,50); s2 := Sym(60)!( 1,24)( 2,23)( 3,22)( 4,21)( 5,28)( 6,27)( 7,26)( 8,25)( 9,32)(10,31)(11,30)(12,29)(13,36)(14,35)(15,34)(16,33)(17,40)(18,39)(19,38)(20,37)(41,44)(42,43)(45,48)(46,47)(49,52)(50,51)(53,56)(54,55)(57,60)(58,59); poly := sub<Sym(60)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.