Overview
- Group
- SmallGroup(720,794)
- Rank
- 3
- Schläfli Type
- {6,60}
- Vertices, edges, …
- 6, 180, 60
- 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
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)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51)(54,55)(58,59);; s1 := ( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(21,41)(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46);; s2 := ( 1,28)( 2,27)( 3,26)( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(41,48)(42,47)(43,46)(44,45)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55);; 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*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(60)!( 2, 3)( 6, 7)(10,11)(14,15)(18,19)(22,23)(26,27)(30,31)(34,35)(38,39)(42,43)(46,47)(50,51)(54,55)(58,59); s1 := Sym(60)!( 2, 4)( 5,17)( 6,20)( 7,19)( 8,18)( 9,13)(10,16)(11,15)(12,14)(21,41)(22,44)(23,43)(24,42)(25,57)(26,60)(27,59)(28,58)(29,53)(30,56)(31,55)(32,54)(33,49)(34,52)(35,51)(36,50)(37,45)(38,48)(39,47)(40,46); s2 := Sym(60)!( 1,28)( 2,27)( 3,26)( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(41,48)(42,47)(43,46)(44,45)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55); 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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.