Overview
- Group
- SmallGroup(768,1089270)
- Rank
- 4
- Schläfli Type
- {24,6,2}
- Vertices, edges, …
- 32, 96, 8, 2
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 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
12-fold
16-fold
24-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92);; s1 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)(32,87)(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,81)(46,82)(47,84)(48,83);; s2 := ( 1, 4)( 5,12)( 6,10)( 7,11)( 8, 9)(13,16)(17,24)(18,22)(19,23)(20,21)(25,28)(29,36)(30,34)(31,35)(32,33)(37,40)(41,48)(42,46)(43,47)(44,45)(49,52)(53,60)(54,58)(55,59)(56,57)(61,64)(65,72)(66,70)(67,71)(68,69)(73,76)(77,84)(78,82)(79,83)(80,81)(85,88)(89,96)(90,94)(91,95)(92,93);; s3 := (97,98);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)(70,91)(71,90)(72,92); s1 := Sym(98)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)(32,87)(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)(44,75)(45,81)(46,82)(47,84)(48,83); s2 := Sym(98)!( 1, 4)( 5,12)( 6,10)( 7,11)( 8, 9)(13,16)(17,24)(18,22)(19,23)(20,21)(25,28)(29,36)(30,34)(31,35)(32,33)(37,40)(41,48)(42,46)(43,47)(44,45)(49,52)(53,60)(54,58)(55,59)(56,57)(61,64)(65,72)(66,70)(67,71)(68,69)(73,76)(77,84)(78,82)(79,83)(80,81)(85,88)(89,96)(90,94)(91,95)(92,93); s3 := Sym(98)!(97,98); poly := sub<Sym(98)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1 >;