Overview
- Group
- SmallGroup(1440,4583)
- Rank
- 5
- Schläfli Type
- {2,2,18,10}
- Vertices, edges, …
- 2, 2, 18, 90, 10
- Order of s0s1s2s3s4
- 90
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
5-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, 7)( 9,10)(12,13)(15,16)(18,19)(20,36)(21,35)(22,37)(23,39)(24,38)(25,40)(26,42)(27,41)(28,43)(29,45)(30,44)(31,46)(32,48)(33,47)(34,49)(51,52)(54,55)(57,58)(60,61)(63,64)(65,81)(66,80)(67,82)(68,84)(69,83)(70,85)(71,87)(72,86)(73,88)(74,90)(75,89)(76,91)(77,93)(78,92)(79,94);; s3 := ( 5,20)( 6,22)( 7,21)( 8,32)( 9,34)(10,33)(11,29)(12,31)(13,30)(14,26)(15,28)(16,27)(17,23)(18,25)(19,24)(35,36)(38,48)(39,47)(40,49)(41,45)(42,44)(43,46)(50,65)(51,67)(52,66)(53,77)(54,79)(55,78)(56,74)(57,76)(58,75)(59,71)(60,73)(61,72)(62,68)(63,70)(64,69)(80,81)(83,93)(84,92)(85,94)(86,90)(87,89)(88,91);; s4 := ( 5,53)( 6,54)( 7,55)( 8,50)( 9,51)(10,52)(11,62)(12,63)(13,64)(14,59)(15,60)(16,61)(17,56)(18,57)(19,58)(20,68)(21,69)(22,70)(23,65)(24,66)(25,67)(26,77)(27,78)(28,79)(29,74)(30,75)(31,76)(32,71)(33,72)(34,73)(35,83)(36,84)(37,85)(38,80)(39,81)(40,82)(41,92)(42,93)(43,94)(44,89)(45,90)(46,91)(47,86)(48,87)(49,88);; 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*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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, 7)( 9,10)(12,13)(15,16)(18,19)(20,36)(21,35)(22,37)(23,39)(24,38)(25,40)(26,42)(27,41)(28,43)(29,45)(30,44)(31,46)(32,48)(33,47)(34,49)(51,52)(54,55)(57,58)(60,61)(63,64)(65,81)(66,80)(67,82)(68,84)(69,83)(70,85)(71,87)(72,86)(73,88)(74,90)(75,89)(76,91)(77,93)(78,92)(79,94); s3 := Sym(94)!( 5,20)( 6,22)( 7,21)( 8,32)( 9,34)(10,33)(11,29)(12,31)(13,30)(14,26)(15,28)(16,27)(17,23)(18,25)(19,24)(35,36)(38,48)(39,47)(40,49)(41,45)(42,44)(43,46)(50,65)(51,67)(52,66)(53,77)(54,79)(55,78)(56,74)(57,76)(58,75)(59,71)(60,73)(61,72)(62,68)(63,70)(64,69)(80,81)(83,93)(84,92)(85,94)(86,90)(87,89)(88,91); s4 := Sym(94)!( 5,53)( 6,54)( 7,55)( 8,50)( 9,51)(10,52)(11,62)(12,63)(13,64)(14,59)(15,60)(16,61)(17,56)(18,57)(19,58)(20,68)(21,69)(22,70)(23,65)(24,66)(25,67)(26,77)(27,78)(28,79)(29,74)(30,75)(31,76)(32,71)(33,72)(34,73)(35,83)(36,84)(37,85)(38,80)(39,81)(40,82)(41,92)(42,93)(43,94)(44,89)(45,90)(46,91)(47,86)(48,87)(49,88); 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*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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 >;