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