Overview
- Group
- SmallGroup(1440,5949)
- Rank
- 5
- Schläfli Type
- {2,2,30,6}
- Vertices, edges, …
- 2, 2, 30, 90, 6
- 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 := (3,4);; s2 := ( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)(34,41)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(65,80)(66,84)(67,83)(68,82)(69,81)(70,90)(71,94)(72,93)(73,92)(74,91)(75,85)(76,89)(77,88)(78,87)(79,86);; s3 := ( 5,71)( 6,70)( 7,74)( 8,73)( 9,72)(10,66)(11,65)(12,69)(13,68)(14,67)(15,76)(16,75)(17,79)(18,78)(19,77)(20,56)(21,55)(22,59)(23,58)(24,57)(25,51)(26,50)(27,54)(28,53)(29,52)(30,61)(31,60)(32,64)(33,63)(34,62)(35,86)(36,85)(37,89)(38,88)(39,87)(40,81)(41,80)(42,84)(43,83)(44,82)(45,91)(46,90)(47,94)(48,93)(49,92);; s4 := (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)(33,48)(34,49)(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)(78,93)(79,94);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(94)!(1,2); s1 := Sym(94)!(3,4); s2 := Sym(94)!( 6, 9)( 7, 8)(10,15)(11,19)(12,18)(13,17)(14,16)(20,35)(21,39)(22,38)(23,37)(24,36)(25,45)(26,49)(27,48)(28,47)(29,46)(30,40)(31,44)(32,43)(33,42)(34,41)(51,54)(52,53)(55,60)(56,64)(57,63)(58,62)(59,61)(65,80)(66,84)(67,83)(68,82)(69,81)(70,90)(71,94)(72,93)(73,92)(74,91)(75,85)(76,89)(77,88)(78,87)(79,86); s3 := Sym(94)!( 5,71)( 6,70)( 7,74)( 8,73)( 9,72)(10,66)(11,65)(12,69)(13,68)(14,67)(15,76)(16,75)(17,79)(18,78)(19,77)(20,56)(21,55)(22,59)(23,58)(24,57)(25,51)(26,50)(27,54)(28,53)(29,52)(30,61)(31,60)(32,64)(33,63)(34,62)(35,86)(36,85)(37,89)(38,88)(39,87)(40,81)(41,80)(42,84)(43,83)(44,82)(45,91)(46,90)(47,94)(48,93)(49,92); s4 := Sym(94)!(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)(33,48)(34,49)(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)(78,93)(79,94); 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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3 >;