Overview
- Group
- SmallGroup(240,177)
- Rank
- 3
- Schläfli Type
- {2,60}
- Vertices, edges, …
- 2, 60, 60
- Order of s0s1s2
- 60
- Order of s0s1s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
6-fold
7-fold
8-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 7)( 8, 9)(11,16)(12,15)(13,18)(14,17)(19,22)(20,21)(23,24)(25,26)(27,28)(29,38)(30,37)(31,36)(32,35)(33,40)(34,39)(41,44)(42,43)(45,48)(46,47)(49,50)(51,58)(52,57)(53,56)(54,55)(59,62)(60,61);; s2 := ( 3,29)( 4,19)( 5,45)( 6,13)( 7,31)( 8,11)( 9,51)(10,35)(12,21)(14,41)(15,27)(16,47)(17,25)(18,59)(20,33)(22,53)(23,30)(24,52)(26,37)(28,55)(32,43)(34,42)(36,49)(38,61)(39,46)(40,60)(44,54)(48,57)(50,56)(58,62);; 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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(62)!(1,2); s1 := Sym(62)!( 4, 5)( 6, 7)( 8, 9)(11,16)(12,15)(13,18)(14,17)(19,22)(20,21)(23,24)(25,26)(27,28)(29,38)(30,37)(31,36)(32,35)(33,40)(34,39)(41,44)(42,43)(45,48)(46,47)(49,50)(51,58)(52,57)(53,56)(54,55)(59,62)(60,61); s2 := Sym(62)!( 3,29)( 4,19)( 5,45)( 6,13)( 7,31)( 8,11)( 9,51)(10,35)(12,21)(14,41)(15,27)(16,47)(17,25)(18,59)(20,33)(22,53)(23,30)(24,52)(26,37)(28,55)(32,43)(34,42)(36,49)(38,61)(39,46)(40,60)(44,54)(48,57)(50,56)(58,62); poly := sub<Sym(62)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;