Overview
- Group
- SmallGroup(1440,5949)
- Rank
- 5
- Schläfli Type
- {2,30,6,2}
- Vertices, edges, …
- 2, 30, 90, 6, 2
- Order of s0s1s2s3s4
- 30
- Order of s0s1s2s3s4s3s2s1
- 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
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(18,33)(19,37)(20,36)(21,35)(22,34)(23,43)(24,47)(25,46)(26,45)(27,44)(28,38)(29,42)(30,41)(31,40)(32,39)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59)(63,78)(64,82)(65,81)(66,80)(67,79)(68,88)(69,92)(70,91)(71,90)(72,89)(73,83)(74,87)(75,86)(76,85)(77,84);; s2 := ( 3,69)( 4,68)( 5,72)( 6,71)( 7,70)( 8,64)( 9,63)(10,67)(11,66)(12,65)(13,74)(14,73)(15,77)(16,76)(17,75)(18,54)(19,53)(20,57)(21,56)(22,55)(23,49)(24,48)(25,52)(26,51)(27,50)(28,59)(29,58)(30,62)(31,61)(32,60)(33,84)(34,83)(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)(45,92)(46,91)(47,90);; s3 := (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);; s4 := (93,94);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s2*s1*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*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(94)!(1,2); s1 := Sym(94)!( 4, 7)( 5, 6)( 8,13)( 9,17)(10,16)(11,15)(12,14)(18,33)(19,37)(20,36)(21,35)(22,34)(23,43)(24,47)(25,46)(26,45)(27,44)(28,38)(29,42)(30,41)(31,40)(32,39)(49,52)(50,51)(53,58)(54,62)(55,61)(56,60)(57,59)(63,78)(64,82)(65,81)(66,80)(67,79)(68,88)(69,92)(70,91)(71,90)(72,89)(73,83)(74,87)(75,86)(76,85)(77,84); s2 := Sym(94)!( 3,69)( 4,68)( 5,72)( 6,71)( 7,70)( 8,64)( 9,63)(10,67)(11,66)(12,65)(13,74)(14,73)(15,77)(16,76)(17,75)(18,54)(19,53)(20,57)(21,56)(22,55)(23,49)(24,48)(25,52)(26,51)(27,50)(28,59)(29,58)(30,62)(31,61)(32,60)(33,84)(34,83)(35,87)(36,86)(37,85)(38,79)(39,78)(40,82)(41,81)(42,80)(43,89)(44,88)(45,92)(46,91)(47,90); s3 := Sym(94)!(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); s4 := Sym(94)!(93,94); poly := sub<Sym(94)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s3*s2*s1*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*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 >;