Overview
- Group
- SmallGroup(360,45)
- Rank
- 3
- Schläfli Type
- {18,10}
- Vertices, edges, …
- 18, 90, 10
- Order of s0s1s2
- 90
- Order of s0s1s2s1
- 2
- Also known as
- {18,10|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-fold
9-fold
10-fold
15-fold
18-fold
30-fold
45-fold
Covers minimal covers in bold
2-fold
3-fold
4-fold
5-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,32)(17,31)(18,33)(19,35)(20,34)(21,36)(22,38)(23,37)(24,39)(25,41)(26,40)(27,42)(28,44)(29,43)(30,45)(47,48)(50,51)(53,54)(56,57)(59,60)(61,77)(62,76)(63,78)(64,80)(65,79)(66,81)(67,83)(68,82)(69,84)(70,86)(71,85)(72,87)(73,89)(74,88)(75,90);; s1 := ( 1,16)( 2,18)( 3,17)( 4,28)( 5,30)( 6,29)( 7,25)( 8,27)( 9,26)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(31,32)(34,44)(35,43)(36,45)(37,41)(38,40)(39,42)(46,61)(47,63)(48,62)(49,73)(50,75)(51,74)(52,70)(53,72)(54,71)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(76,77)(79,89)(80,88)(81,90)(82,86)(83,85)(84,87);; s2 := ( 1,49)( 2,50)( 3,51)( 4,46)( 5,47)( 6,48)( 7,58)( 8,59)( 9,60)(10,55)(11,56)(12,57)(13,52)(14,53)(15,54)(16,64)(17,65)(18,66)(19,61)(20,62)(21,63)(22,73)(23,74)(24,75)(25,70)(26,71)(27,72)(28,67)(29,68)(30,69)(31,79)(32,80)(33,81)(34,76)(35,77)(36,78)(37,88)(38,89)(39,90)(40,85)(41,86)(42,87)(43,82)(44,83)(45,84);; 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*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(90)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(16,32)(17,31)(18,33)(19,35)(20,34)(21,36)(22,38)(23,37)(24,39)(25,41)(26,40)(27,42)(28,44)(29,43)(30,45)(47,48)(50,51)(53,54)(56,57)(59,60)(61,77)(62,76)(63,78)(64,80)(65,79)(66,81)(67,83)(68,82)(69,84)(70,86)(71,85)(72,87)(73,89)(74,88)(75,90); s1 := Sym(90)!( 1,16)( 2,18)( 3,17)( 4,28)( 5,30)( 6,29)( 7,25)( 8,27)( 9,26)(10,22)(11,24)(12,23)(13,19)(14,21)(15,20)(31,32)(34,44)(35,43)(36,45)(37,41)(38,40)(39,42)(46,61)(47,63)(48,62)(49,73)(50,75)(51,74)(52,70)(53,72)(54,71)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65)(76,77)(79,89)(80,88)(81,90)(82,86)(83,85)(84,87); s2 := Sym(90)!( 1,49)( 2,50)( 3,51)( 4,46)( 5,47)( 6,48)( 7,58)( 8,59)( 9,60)(10,55)(11,56)(12,57)(13,52)(14,53)(15,54)(16,64)(17,65)(18,66)(19,61)(20,62)(21,63)(22,73)(23,74)(24,75)(25,70)(26,71)(27,72)(28,67)(29,68)(30,69)(31,79)(32,80)(33,81)(34,76)(35,77)(36,78)(37,88)(38,89)(39,90)(40,85)(41,86)(42,87)(43,82)(44,83)(45,84); 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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.