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