Overview
- Group
- SmallGroup(720,810)
- Rank
- 3
- Schläfli Type
- {6,20}
- Vertices, edges, …
- 18, 180, 60
- Order of s0s1s2
- 20
- 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
5-fold
9-fold
10-fold
18-fold
36-fold
45-fold
90-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 := ( 1,46)( 2,47)( 3,48)( 4,49)( 5,50)( 6,56)( 7,57)( 8,58)( 9,59)(10,60)(11,51)(12,52)(13,53)(14,54)(15,55)(16,76)(17,77)(18,78)(19,79)(20,80)(21,86)(22,87)(23,88)(24,89)(25,90)(26,81)(27,82)(28,83)(29,84)(30,85)(31,61)(32,62)(33,63)(34,64)(35,65)(36,71)(37,72)(38,73)(39,74)(40,75)(41,66)(42,67)(43,68)(44,69)(45,70);; s1 := ( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44)(46,51)(47,55)(48,54)(49,53)(50,52)(57,60)(58,59)(61,66)(62,70)(63,69)(64,68)(65,67)(72,75)(73,74)(76,81)(77,85)(78,84)(79,83)(80,82)(87,90)(88,89);; s2 := ( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)(13,35)(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45)(46,47)(48,50)(51,62)(52,61)(53,65)(54,64)(55,63)(56,77)(57,76)(58,80)(59,79)(60,78)(66,67)(68,70)(71,82)(72,81)(73,85)(74,84)(75,83)(86,87)(88,90);; 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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
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(90)!( 1,46)( 2,47)( 3,48)( 4,49)( 5,50)( 6,56)( 7,57)( 8,58)( 9,59)(10,60)(11,51)(12,52)(13,53)(14,54)(15,55)(16,76)(17,77)(18,78)(19,79)(20,80)(21,86)(22,87)(23,88)(24,89)(25,90)(26,81)(27,82)(28,83)(29,84)(30,85)(31,61)(32,62)(33,63)(34,64)(35,65)(36,71)(37,72)(38,73)(39,74)(40,75)(41,66)(42,67)(43,68)(44,69)(45,70); s1 := Sym(90)!( 1, 6)( 2,10)( 3, 9)( 4, 8)( 5, 7)(12,15)(13,14)(16,21)(17,25)(18,24)(19,23)(20,22)(27,30)(28,29)(31,36)(32,40)(33,39)(34,38)(35,37)(42,45)(43,44)(46,51)(47,55)(48,54)(49,53)(50,52)(57,60)(58,59)(61,66)(62,70)(63,69)(64,68)(65,67)(72,75)(73,74)(76,81)(77,85)(78,84)(79,83)(80,82)(87,90)(88,89); s2 := Sym(90)!( 1, 2)( 3, 5)( 6,17)( 7,16)( 8,20)( 9,19)(10,18)(11,32)(12,31)(13,35)(14,34)(15,33)(21,22)(23,25)(26,37)(27,36)(28,40)(29,39)(30,38)(41,42)(43,45)(46,47)(48,50)(51,62)(52,61)(53,65)(54,64)(55,63)(56,77)(57,76)(58,80)(59,79)(60,78)(66,67)(68,70)(71,82)(72,81)(73,85)(74,84)(75,83)(86,87)(88,90); poly := sub<Sym(90)|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*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, 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 >;
References
None.
to this polytope.