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Polytope of Type {2,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6}*768a
if this polytope has a name.
Group : SmallGroup(768,1089108)
Rank : 4
Schlafli Type : {2,4,6}
Number of vertices, edges, etc : 2, 32, 96, 48
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 : {2,4,6}*384a
   4-fold quotients : {2,4,6}*192
   8-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   16-fold quotients : {2,4,3}*48, {2,2,6}*48
   32-fold quotients : {2,2,3}*24
   48-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,65)(10,66)(11,51)(12,52)
(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,75)(20,76)(21,77)(22,78)(23,79)
(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)(34,74)
(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,83)(44,84)(45,85)
(46,86)(47,87)(48,88)(49,89)(50,90);;
s2 := ( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)(22,37)
(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)(33,49)
(34,50)(53,54)(55,62)(56,61)(57,59)(58,60)(63,64)(67,83)(68,84)(69,86)(70,85)
(71,94)(72,93)(73,91)(74,92)(75,89)(76,90)(77,88)(78,87)(79,96)(80,95)(81,97)
(82,98);;
s3 := ( 3,35)( 4,37)( 5,36)( 6,38)( 7,47)( 8,49)( 9,48)(10,50)(11,43)(12,45)
(13,44)(14,46)(15,39)(16,41)(17,40)(18,42)(20,21)(23,31)(24,33)(25,32)(26,34)
(28,29)(51,83)(52,85)(53,84)(54,86)(55,95)(56,97)(57,96)(58,98)(59,91)(60,93)
(61,92)(62,94)(63,87)(64,89)(65,88)(66,90)(68,69)(71,79)(72,81)(73,80)(74,82)
(76,77);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(98)!(1,2);
s1 := Sym(98)!( 3,59)( 4,60)( 5,61)( 6,62)( 7,63)( 8,64)( 9,65)(10,66)(11,51)
(12,52)(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,75)(20,76)(21,77)(22,78)
(23,79)(24,80)(25,81)(26,82)(27,67)(28,68)(29,69)(30,70)(31,71)(32,72)(33,73)
(34,74)(35,91)(36,92)(37,93)(38,94)(39,95)(40,96)(41,97)(42,98)(43,83)(44,84)
(45,85)(46,86)(47,87)(48,88)(49,89)(50,90);
s2 := Sym(98)!( 5, 6)( 7,14)( 8,13)( 9,11)(10,12)(15,16)(19,35)(20,36)(21,38)
(22,37)(23,46)(24,45)(25,43)(26,44)(27,41)(28,42)(29,40)(30,39)(31,48)(32,47)
(33,49)(34,50)(53,54)(55,62)(56,61)(57,59)(58,60)(63,64)(67,83)(68,84)(69,86)
(70,85)(71,94)(72,93)(73,91)(74,92)(75,89)(76,90)(77,88)(78,87)(79,96)(80,95)
(81,97)(82,98);
s3 := Sym(98)!( 3,35)( 4,37)( 5,36)( 6,38)( 7,47)( 8,49)( 9,48)(10,50)(11,43)
(12,45)(13,44)(14,46)(15,39)(16,41)(17,40)(18,42)(20,21)(23,31)(24,33)(25,32)
(26,34)(28,29)(51,83)(52,85)(53,84)(54,86)(55,95)(56,97)(57,96)(58,98)(59,91)
(60,93)(61,92)(62,94)(63,87)(64,89)(65,88)(66,90)(68,69)(71,79)(72,81)(73,80)
(74,82)(76,77);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >; 
 

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