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