Overview
- Group
- SmallGroup(768,1089108)
- Rank
- 5
- Schläfli Type
- {6,3,4,2}
- Vertices, edges, …
- 8, 24, 16, 8, 2
- 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 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)(20,35)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)(31,48)(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)(68,83)(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)(79,96)(80,95);; s1 := ( 1,65)( 2,68)( 3,67)( 4,66)( 5,69)( 6,72)( 7,71)( 8,70)( 9,77)(10,80)(11,79)(12,78)(13,73)(14,76)(15,75)(16,74)(17,49)(18,52)(19,51)(20,50)(21,53)(22,56)(23,55)(24,54)(25,61)(26,64)(27,63)(28,62)(29,57)(30,60)(31,59)(32,58)(33,81)(34,84)(35,83)(36,82)(37,85)(38,88)(39,87)(40,86)(41,93)(42,96)(43,95)(44,94)(45,89)(46,92)(47,91)(48,90);; s2 := ( 1,61)( 2,62)( 3,64)( 4,63)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,49)(14,50)(15,52)(16,51)(17,93)(18,94)(19,96)(20,95)(21,85)(22,86)(23,88)(24,87)(25,89)(26,90)(27,92)(28,91)(29,81)(30,82)(31,84)(32,83)(33,77)(34,78)(35,80)(36,79)(37,69)(38,70)(39,72)(40,71)(41,73)(42,74)(43,76)(44,75)(45,65)(46,66)(47,68)(48,67);; s3 := ( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)(26,27)(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)(57,60)(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80)(85,87)(86,88)(89,92)(90,91)(93,94)(95,96);; s4 := (97,98);; 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*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,
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s2*s1*s2*s3*s2*s1*s3*s2*s3*s0*s1*s2*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)(20,35)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)(31,48)(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)(68,83)(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)(79,96)(80,95); s1 := Sym(98)!( 1,65)( 2,68)( 3,67)( 4,66)( 5,69)( 6,72)( 7,71)( 8,70)( 9,77)(10,80)(11,79)(12,78)(13,73)(14,76)(15,75)(16,74)(17,49)(18,52)(19,51)(20,50)(21,53)(22,56)(23,55)(24,54)(25,61)(26,64)(27,63)(28,62)(29,57)(30,60)(31,59)(32,58)(33,81)(34,84)(35,83)(36,82)(37,85)(38,88)(39,87)(40,86)(41,93)(42,96)(43,95)(44,94)(45,89)(46,92)(47,91)(48,90); s2 := Sym(98)!( 1,61)( 2,62)( 3,64)( 4,63)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)(11,60)(12,59)(13,49)(14,50)(15,52)(16,51)(17,93)(18,94)(19,96)(20,95)(21,85)(22,86)(23,88)(24,87)(25,89)(26,90)(27,92)(28,91)(29,81)(30,82)(31,84)(32,83)(33,77)(34,78)(35,80)(36,79)(37,69)(38,70)(39,72)(40,71)(41,73)(42,74)(43,76)(44,75)(45,65)(46,66)(47,68)(48,67); s3 := Sym(98)!( 5, 7)( 6, 8)( 9,12)(10,11)(13,14)(15,16)(21,23)(22,24)(25,28)(26,27)(29,30)(31,32)(37,39)(38,40)(41,44)(42,43)(45,46)(47,48)(53,55)(54,56)(57,60)(58,59)(61,62)(63,64)(69,71)(70,72)(73,76)(74,75)(77,78)(79,80)(85,87)(86,88)(89,92)(90,91)(93,94)(95,96); s4 := Sym(98)!(97,98); 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*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, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s3*s2*s1*s3*s2*s3*s0*s1*s2*s3*s2*s1 >;