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Polytope of Type {4,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2}*768a
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 32, 96, 48, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 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 : {4,6,2}*384a
   4-fold quotients : {4,6,2}*192
   8-fold quotients : {4,3,2}*96, {4,6,2}*96b, {4,6,2}*96c
   16-fold quotients : {4,3,2}*48, {2,6,2}*48
   32-fold quotients : {2,3,2}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)(10,50)
(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)(21,77)
(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)
(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)(43,83)
(44,84)(45,85)(46,86)(47,87)(48,88);;
s1 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)
(32,48)(51,52)(53,60)(54,59)(55,57)(56,58)(61,62)(65,81)(66,82)(67,84)(68,83)
(69,92)(70,91)(71,89)(72,90)(73,87)(74,88)(75,86)(76,85)(77,94)(78,93)(79,95)
(80,96);;
s2 := ( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)(10,43)
(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)(24,32)
(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)(58,91)
(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)(72,80)
(74,75);;
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*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!( 1,57)( 2,58)( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,49)
(10,50)(11,51)(12,52)(13,53)(14,54)(15,55)(16,56)(17,73)(18,74)(19,75)(20,76)
(21,77)(22,78)(23,79)(24,80)(25,65)(26,66)(27,67)(28,68)(29,69)(30,70)(31,71)
(32,72)(33,89)(34,90)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,81)(42,82)
(43,83)(44,84)(45,85)(46,86)(47,87)(48,88);
s1 := Sym(98)!( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)
(20,35)(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)
(31,47)(32,48)(51,52)(53,60)(54,59)(55,57)(56,58)(61,62)(65,81)(66,82)(67,84)
(68,83)(69,92)(70,91)(71,89)(72,90)(73,87)(74,88)(75,86)(76,85)(77,94)(78,93)
(79,95)(80,96);
s2 := Sym(98)!( 1,33)( 2,35)( 3,34)( 4,36)( 5,45)( 6,47)( 7,46)( 8,48)( 9,41)
(10,43)(11,42)(12,44)(13,37)(14,39)(15,38)(16,40)(18,19)(21,29)(22,31)(23,30)
(24,32)(26,27)(49,81)(50,83)(51,82)(52,84)(53,93)(54,95)(55,94)(56,96)(57,89)
(58,91)(59,90)(60,92)(61,85)(62,87)(63,86)(64,88)(66,67)(69,77)(70,79)(71,78)
(72,80)(74,75);
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

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