Overview
- Group
- SmallGroup(960,10889)
- Rank
- 3
- Schläfli Type
- {6,20}
- Vertices, edges, …
- 24, 240, 80
- Order of s0s1s2
- 20
- Order of s0s1s2s1
- 20
- 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
16-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 := ( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42);; s1 := ( 1, 2)( 3,31)( 4,25)( 5,27)( 6,10)( 8,17)( 9,19)(11,12)(13,43)(14,32)(15,28)(16,24)(18,26)(20,38)(21,40)(22,42)(29,44)(30,34)(33,35)(45,47)(49,50);; s2 := ( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)(11,21)(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)(35,39)(36,47)(38,48)(45,46);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(50)!( 2,45)( 3,41)( 4,17)( 5,19)( 7,30)( 8,48)( 9,36)(10,47)(11,23)(12,34)(13,22)(14,40)(15,39)(20,26)(21,29)(24,38)(25,37)(27,46)(28,31)(35,42); s1 := Sym(50)!( 1, 2)( 3,31)( 4,25)( 5,27)( 6,10)( 8,17)( 9,19)(11,12)(13,43)(14,32)(15,28)(16,24)(18,26)(20,38)(21,40)(22,42)(29,44)(30,34)(33,35)(45,47)(49,50); s2 := Sym(50)!( 1,32)( 2,27)( 3,22)( 4,34)( 5,28)( 6,44)( 7,14)( 8,24)( 9,10)(11,21)(12,17)(13,41)(15,42)(16,33)(18,43)(19,31)(20,37)(23,29)(25,26)(30,40)(35,39)(36,47)(38,48)(45,46); poly := sub<Sym(50)|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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;
References
None.
to this polytope.