Overview
- Group
- SmallGroup(960,10869)
- Rank
- 3
- Schläfli Type
- {10,8}
- Vertices, edges, …
- 60, 240, 48
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
120-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42);; s1 := ( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)(17,29)(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39);; s2 := ( 3,23)( 4,24)( 5,26)( 6,25)( 7,36)( 8,35)( 9,38)(10,37)(11,12)(15,21)(16,22)(17,20)(18,19)(27,28)(33,34)(39,42)(40,41);; 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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(42)!( 3,25)( 4,26)( 5,24)( 6,23)( 7,16)( 8,15)( 9,17)(10,18)(19,37)(20,38)(21,35)(22,36)(27,33)(28,34)(29,31)(30,32)(39,40)(41,42); s1 := Sym(42)!( 1, 2)( 7, 8)( 9,10)(11,19)(12,20)(13,21)(14,22)(15,27)(16,28)(17,29)(18,30)(23,35)(24,36)(25,37)(26,38)(31,42)(32,41)(33,40)(34,39); s2 := Sym(42)!( 3,23)( 4,24)( 5,26)( 6,25)( 7,36)( 8,35)( 9,38)(10,37)(11,12)(15,21)(16,22)(17,20)(18,19)(27,28)(33,34)(39,42)(40,41); poly := sub<Sym(42)|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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References
None.
to this polytope.