Overview
- Group
- SmallGroup(960,10877)
- Rank
- 3
- Schläfli Type
- {6,20}
- Vertices, edges, …
- 24, 240, 80
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 8
- 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 := ( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68);; s1 := ( 2,36)( 3,27)( 4,35)( 5,37)( 6,66)( 7,61)( 8,63)( 9,69)(10,46)(11,47)(12,45)(13,43)(14,44)(15,64)(16,71)(18,48)(19,70)(21,54)(22,32)(23,73)(24,74)(26,75)(28,38)(29,76)(30,40)(31,77)(33,39)(41,80)(42,78)(49,58)(50,57)(51,56)(52,53)(55,79)(59,72)(60,67);; s2 := ( 1,44)( 2,11)( 3,48)( 4,63)( 5,13)( 6,27)( 7,20)( 8,74)( 9,26)(10,42)(12,31)(14,55)(15,36)(16,41)(17,38)(18,30)(19,23)(21,46)(22,43)(24,66)(25,71)(28,57)(29,59)(32,72)(33,56)(34,49)(35,65)(37,45)(39,60)(40,50)(47,80)(51,52)(53,61)(54,67)(58,78)(62,73)(64,75)(68,77)(69,79)(70,76);; 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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(80)!( 1, 5)( 2,41)( 3,32)( 4,54)( 6,43)( 7,18)( 9,14)(10,47)(11,16)(12,64)(13,44)(15,19)(17,62)(20,30)(21,53)(22,27)(23,36)(24,34)(25,29)(26,55)(28,39)(31,75)(33,78)(35,77)(37,76)(38,73)(42,80)(45,70)(46,61)(48,72)(49,66)(51,69)(52,79)(56,58)(57,60)(59,71)(63,67)(65,68); s1 := Sym(80)!( 2,36)( 3,27)( 4,35)( 5,37)( 6,66)( 7,61)( 8,63)( 9,69)(10,46)(11,47)(12,45)(13,43)(14,44)(15,64)(16,71)(18,48)(19,70)(21,54)(22,32)(23,73)(24,74)(26,75)(28,38)(29,76)(30,40)(31,77)(33,39)(41,80)(42,78)(49,58)(50,57)(51,56)(52,53)(55,79)(59,72)(60,67); s2 := Sym(80)!( 1,44)( 2,11)( 3,48)( 4,63)( 5,13)( 6,27)( 7,20)( 8,74)( 9,26)(10,42)(12,31)(14,55)(15,36)(16,41)(17,38)(18,30)(19,23)(21,46)(22,43)(24,66)(25,71)(28,57)(29,59)(32,72)(33,56)(34,49)(35,65)(37,45)(39,60)(40,50)(47,80)(51,52)(53,61)(54,67)(58,78)(62,73)(64,75)(68,77)(69,79)(70,76); poly := sub<Sym(80)|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*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1 >;
References
None.
to this polytope.