Overview
- Group
- SmallGroup(720,402)
- Rank
- 4
- Schläfli Type
- {10,18,2}
- Vertices, edges, …
- 10, 90, 18, 2
- Order of s0s1s2s3
- 90
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- 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
Representations
Permutation Representation (GAP)
s0 := ( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(19,28)(20,29)(21,30)(22,25)(23,26)(24,27)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57)(64,73)(65,74)(66,75)(67,70)(68,71)(69,72)(79,88)(80,89)(81,90)(82,85)(83,86)(84,87);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,35)(17,34)(18,36)(19,32)(20,31)(21,33)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,38)(29,37)(30,39)(46,49)(47,51)(48,50)(52,58)(53,60)(54,59)(56,57)(61,80)(62,79)(63,81)(64,77)(65,76)(66,78)(67,89)(68,88)(69,90)(70,86)(71,85)(72,87)(73,83)(74,82)(75,84);; s2 := ( 1,61)( 2,63)( 3,62)( 4,64)( 5,66)( 6,65)( 7,67)( 8,69)( 9,68)(10,70)(11,72)(12,71)(13,73)(14,75)(15,74)(16,46)(17,48)(18,47)(19,49)(20,51)(21,50)(22,52)(23,54)(24,53)(25,55)(26,57)(27,56)(28,58)(29,60)(30,59)(31,77)(32,76)(33,78)(34,80)(35,79)(36,81)(37,83)(38,82)(39,84)(40,86)(41,85)(42,87)(43,89)(44,88)(45,90);; s3 := (91,92);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(92)!( 4,13)( 5,14)( 6,15)( 7,10)( 8,11)( 9,12)(19,28)(20,29)(21,30)(22,25)(23,26)(24,27)(34,43)(35,44)(36,45)(37,40)(38,41)(39,42)(49,58)(50,59)(51,60)(52,55)(53,56)(54,57)(64,73)(65,74)(66,75)(67,70)(68,71)(69,72)(79,88)(80,89)(81,90)(82,85)(83,86)(84,87); s1 := Sym(92)!( 1, 4)( 2, 6)( 3, 5)( 7,13)( 8,15)( 9,14)(11,12)(16,35)(17,34)(18,36)(19,32)(20,31)(21,33)(22,44)(23,43)(24,45)(25,41)(26,40)(27,42)(28,38)(29,37)(30,39)(46,49)(47,51)(48,50)(52,58)(53,60)(54,59)(56,57)(61,80)(62,79)(63,81)(64,77)(65,76)(66,78)(67,89)(68,88)(69,90)(70,86)(71,85)(72,87)(73,83)(74,82)(75,84); s2 := Sym(92)!( 1,61)( 2,63)( 3,62)( 4,64)( 5,66)( 6,65)( 7,67)( 8,69)( 9,68)(10,70)(11,72)(12,71)(13,73)(14,75)(15,74)(16,46)(17,48)(18,47)(19,49)(20,51)(21,50)(22,52)(23,54)(24,53)(25,55)(26,57)(27,56)(28,58)(29,60)(30,59)(31,77)(32,76)(33,78)(34,80)(35,79)(36,81)(37,83)(38,82)(39,84)(40,86)(41,85)(42,87)(43,89)(44,88)(45,90); s3 := Sym(92)!(91,92); poly := sub<Sym(92)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;