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