Overview
- Group
- SmallGroup(768,1089108)
- Rank
- 5
- Schläfli Type
- {2,4,6,3}
- Vertices, edges, …
- 2, 8, 32, 24, 4
- Order of s0s1s2s3s4
- 4
- 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
4-fold
8-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98);; s2 := ( 3,23)( 4,26)( 5,25)( 6,24)( 7,19)( 8,22)( 9,21)(10,20)(11,27)(12,30)(13,29)(14,28)(15,31)(16,34)(17,33)(18,32)(35,39)(36,42)(37,41)(38,40)(44,46)(48,50)(51,71)(52,74)(53,73)(54,72)(55,67)(56,70)(57,69)(58,68)(59,75)(60,78)(61,77)(62,76)(63,79)(64,82)(65,81)(66,80)(83,87)(84,90)(85,89)(86,88)(92,94)(96,98);; s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,63)(16,64)(17,66)(18,65)(19,83)(20,84)(21,86)(22,85)(23,91)(24,92)(25,94)(26,93)(27,87)(28,88)(29,90)(30,89)(31,95)(32,96)(33,98)(34,97)(35,67)(36,68)(37,70)(38,69)(39,75)(40,76)(41,78)(42,77)(43,71)(44,72)(45,74)(46,73)(47,79)(48,80)(49,82)(50,81);; s4 := ( 3,67)( 4,70)( 5,69)( 6,68)( 7,71)( 8,74)( 9,73)(10,72)(11,79)(12,82)(13,81)(14,80)(15,75)(16,78)(17,77)(18,76)(19,51)(20,54)(21,53)(22,52)(23,55)(24,58)(25,57)(26,56)(27,63)(28,66)(29,65)(30,64)(31,59)(32,62)(33,61)(34,60)(35,83)(36,86)(37,85)(38,84)(39,87)(40,90)(41,89)(42,88)(43,95)(44,98)(45,97)(46,96)(47,91)(48,94)(49,93)(50,92);; 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*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s4*s1*s2*s3*s4*s2*s1*s2*s3*s4*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 7, 9)( 8,10)(11,14)(12,13)(15,16)(17,18)(23,25)(24,26)(27,30)(28,29)(31,32)(33,34)(39,41)(40,42)(43,46)(44,45)(47,48)(49,50)(55,57)(56,58)(59,62)(60,61)(63,64)(65,66)(71,73)(72,74)(75,78)(76,77)(79,80)(81,82)(87,89)(88,90)(91,94)(92,93)(95,96)(97,98); s2 := Sym(98)!( 3,23)( 4,26)( 5,25)( 6,24)( 7,19)( 8,22)( 9,21)(10,20)(11,27)(12,30)(13,29)(14,28)(15,31)(16,34)(17,33)(18,32)(35,39)(36,42)(37,41)(38,40)(44,46)(48,50)(51,71)(52,74)(53,73)(54,72)(55,67)(56,70)(57,69)(58,68)(59,75)(60,78)(61,77)(62,76)(63,79)(64,82)(65,81)(66,80)(83,87)(84,90)(85,89)(86,88)(92,94)(96,98); s3 := Sym(98)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,63)(16,64)(17,66)(18,65)(19,83)(20,84)(21,86)(22,85)(23,91)(24,92)(25,94)(26,93)(27,87)(28,88)(29,90)(30,89)(31,95)(32,96)(33,98)(34,97)(35,67)(36,68)(37,70)(38,69)(39,75)(40,76)(41,78)(42,77)(43,71)(44,72)(45,74)(46,73)(47,79)(48,80)(49,82)(50,81); s4 := Sym(98)!( 3,67)( 4,70)( 5,69)( 6,68)( 7,71)( 8,74)( 9,73)(10,72)(11,79)(12,82)(13,81)(14,80)(15,75)(16,78)(17,77)(18,76)(19,51)(20,54)(21,53)(22,52)(23,55)(24,58)(25,57)(26,56)(27,63)(28,66)(29,65)(30,64)(31,59)(32,62)(33,61)(34,60)(35,83)(36,86)(37,85)(38,84)(39,87)(40,90)(41,89)(42,88)(43,95)(44,98)(45,97)(46,96)(47,91)(48,94)(49,93)(50,92); poly := sub<Sym(98)|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*s4, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s4*s3*s2*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s4*s1*s2*s3*s4*s2*s1*s2*s3*s4*s1*s2 >;