Overview
- Group
- SmallGroup(720,831)
- Rank
- 4
- Schläfli Type
- {6,30,2}
- Vertices, edges, …
- 6, 90, 30, 2
- Order of s0s1s2s3
- 30
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
5-fold
6-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 := (16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90);; s1 := ( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)(40,42)(46,61)(47,65)(48,64)(49,63)(50,62)(51,71)(52,75)(53,74)(54,73)(55,72)(56,66)(57,70)(58,69)(59,68)(60,67)(77,80)(78,79)(81,86)(82,90)(83,89)(84,88)(85,87);; s2 := ( 1,52)( 2,51)( 3,55)( 4,54)( 5,53)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)(11,57)(12,56)(13,60)(14,59)(15,58)(16,82)(17,81)(18,85)(19,84)(20,83)(21,77)(22,76)(23,80)(24,79)(25,78)(26,87)(27,86)(28,90)(29,89)(30,88)(31,67)(32,66)(33,70)(34,69)(35,68)(36,62)(37,61)(38,65)(39,64)(40,63)(41,72)(42,71)(43,75)(44,74)(45,73);; 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*s0*s1*s0*s1*s2*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*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)!(16,31)(17,32)(18,33)(19,34)(20,35)(21,36)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,43)(29,44)(30,45)(61,76)(62,77)(63,78)(64,79)(65,80)(66,81)(67,82)(68,83)(69,84)(70,85)(71,86)(72,87)(73,88)(74,89)(75,90); s1 := Sym(92)!( 1,16)( 2,20)( 3,19)( 4,18)( 5,17)( 6,26)( 7,30)( 8,29)( 9,28)(10,27)(11,21)(12,25)(13,24)(14,23)(15,22)(32,35)(33,34)(36,41)(37,45)(38,44)(39,43)(40,42)(46,61)(47,65)(48,64)(49,63)(50,62)(51,71)(52,75)(53,74)(54,73)(55,72)(56,66)(57,70)(58,69)(59,68)(60,67)(77,80)(78,79)(81,86)(82,90)(83,89)(84,88)(85,87); s2 := Sym(92)!( 1,52)( 2,51)( 3,55)( 4,54)( 5,53)( 6,47)( 7,46)( 8,50)( 9,49)(10,48)(11,57)(12,56)(13,60)(14,59)(15,58)(16,82)(17,81)(18,85)(19,84)(20,83)(21,77)(22,76)(23,80)(24,79)(25,78)(26,87)(27,86)(28,90)(29,89)(30,88)(31,67)(32,66)(33,70)(34,69)(35,68)(36,62)(37,61)(38,65)(39,64)(40,63)(41,72)(42,71)(43,75)(44,74)(45,73); 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*s0*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;