Polytope of Type {4,6,3,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,3,2}*768b
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 5
Schlafli Type : {4,6,3,2}
Number of vertices, edges, etc : 8, 32, 24, 4, 2
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 : {4,3,3,2}*384
4-fold quotients : {2,6,3,2}*192
8-fold quotients : {2,3,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
s1 := ( 1,21)( 2,24)( 3,23)( 4,22)( 5,17)( 6,20)( 7,19)( 8,18)( 9,25)(10,28)
(11,27)(12,26)(13,29)(14,32)(15,31)(16,30)(33,37)(34,40)(35,39)(36,38)(42,44)
(46,48)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66)(57,73)(58,76)
(59,75)(60,74)(61,77)(62,80)(63,79)(64,78)(81,85)(82,88)(83,87)(84,86)(90,92)
(94,96);;
s2 := ( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)(10,54)
(11,56)(12,55)(13,61)(14,62)(15,64)(16,63)(17,81)(18,82)(19,84)(20,83)(21,89)
(22,90)(23,92)(24,91)(25,85)(26,86)(27,88)(28,87)(29,93)(30,94)(31,96)(32,95)
(33,65)(34,66)(35,68)(36,67)(37,73)(38,74)(39,76)(40,75)(41,69)(42,70)(43,72)
(44,71)(45,77)(46,78)(47,80)(48,79);;
s3 := ( 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);;
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,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s0*s2*s1*s0*s1*s3*s2*s1*s3*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
s1 := Sym(98)!( 1,21)( 2,24)( 3,23)( 4,22)( 5,17)( 6,20)( 7,19)( 8,18)( 9,25)
(10,28)(11,27)(12,26)(13,29)(14,32)(15,31)(16,30)(33,37)(34,40)(35,39)(36,38)
(42,44)(46,48)(49,69)(50,72)(51,71)(52,70)(53,65)(54,68)(55,67)(56,66)(57,73)
(58,76)(59,75)(60,74)(61,77)(62,80)(63,79)(64,78)(81,85)(82,88)(83,87)(84,86)
(90,92)(94,96);
s2 := Sym(98)!( 1,49)( 2,50)( 3,52)( 4,51)( 5,57)( 6,58)( 7,60)( 8,59)( 9,53)
(10,54)(11,56)(12,55)(13,61)(14,62)(15,64)(16,63)(17,81)(18,82)(19,84)(20,83)
(21,89)(22,90)(23,92)(24,91)(25,85)(26,86)(27,88)(28,87)(29,93)(30,94)(31,96)
(32,95)(33,65)(34,66)(35,68)(36,67)(37,73)(38,74)(39,76)(40,75)(41,69)(42,70)
(43,72)(44,71)(45,77)(46,78)(47,80)(48,79);
s3 := 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);
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, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s0*s2*s1*s0*s1*s3*s2*s1*s3*s0*s1*s2*s1*s0*s1 >;
to this polytope