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