Overview
- Group
- SmallGroup(720,831)
- Rank
- 4
- Schläfli Type
- {2,6,30}
- Vertices, edges, …
- 2, 6, 90, 30
- 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 := (1,2);; s1 := (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)(31,46)(32,47)(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)(76,91)(77,92);; s2 := ( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89);; s3 := ( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,84)(19,83)(20,87)(21,86)(22,85)(23,79)(24,78)(25,82)(26,81)(27,80)(28,89)(29,88)(30,92)(31,91)(32,90)(33,69)(34,68)(35,72)(36,71)(37,70)(38,64)(39,63)(40,67)(41,66)(42,65)(43,74)(44,73)(45,77)(46,76)(47,75);; 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*s1*s2*s1*s2*s3*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*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)!(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)(31,46)(32,47)(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)(76,91)(77,92); s2 := Sym(92)!( 3,18)( 4,22)( 5,21)( 6,20)( 7,19)( 8,28)( 9,32)(10,31)(11,30)(12,29)(13,23)(14,27)(15,26)(16,25)(17,24)(34,37)(35,36)(38,43)(39,47)(40,46)(41,45)(42,44)(48,63)(49,67)(50,66)(51,65)(52,64)(53,73)(54,77)(55,76)(56,75)(57,74)(58,68)(59,72)(60,71)(61,70)(62,69)(79,82)(80,81)(83,88)(84,92)(85,91)(86,90)(87,89); s3 := Sym(92)!( 3,54)( 4,53)( 5,57)( 6,56)( 7,55)( 8,49)( 9,48)(10,52)(11,51)(12,50)(13,59)(14,58)(15,62)(16,61)(17,60)(18,84)(19,83)(20,87)(21,86)(22,85)(23,79)(24,78)(25,82)(26,81)(27,80)(28,89)(29,88)(30,92)(31,91)(32,90)(33,69)(34,68)(35,72)(36,71)(37,70)(38,64)(39,63)(40,67)(41,66)(42,65)(43,74)(44,73)(45,77)(46,76)(47,75); 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*s1*s2*s1*s2*s3*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;