Polytope of Type {2,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,3}*768b
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 5
Schlafli Type : {2,4,6,3}
Number of vertices, edges, etc : 2, 8, 32, 24, 4
Order of s0s1s2s3s4 : 4
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,3,3}*384
4-fold quotients : {2,2,6,3}*192
8-fold quotients : {2,2,3,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
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*s4*s3*s2*s4*s3*s2*s4*s3*s2*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,
s4*s1*s3*s2*s1*s2*s4*s3*s2*s4*s1*s2*s3*s2*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*s4*s3*s2*s4*s3*s2*s4*s3*s2*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,
s4*s1*s3*s2*s1*s2*s4*s3*s2*s4*s1*s2*s3*s2*s1*s2 >;
to this polytope