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Polytope of Type {2,96,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,96,2}*768
if this polytope has a name.
Group : SmallGroup(768,327684)
Rank : 4
Schlafli Type : {2,96,2}
Number of vertices, edges, etc : 2, 96, 96, 2
Order of s0s1s2s3 : 96
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,48,2}*384
   3-fold quotients : {2,32,2}*256
   4-fold quotients : {2,24,2}*192
   6-fold quotients : {2,16,2}*128
   8-fold quotients : {2,12,2}*96
   12-fold quotients : {2,8,2}*64
   16-fold quotients : {2,6,2}*48
   24-fold quotients : {2,4,2}*32
   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 := (1,2);;
s1 := ( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,21)(16,23)(17,22)(18,24)(19,26)
(20,25)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)(36,45)
(37,47)(38,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,84)(58,86)(59,85)
(60,81)(61,83)(62,82)(63,93)(64,95)(65,94)(66,96)(67,98)(68,97)(69,87)(70,89)
(71,88)(72,90)(73,92)(74,91);;
s2 := ( 3,52)( 4,51)( 5,53)( 6,55)( 7,54)( 8,56)( 9,61)(10,60)(11,62)(12,58)
(13,57)(14,59)(15,70)(16,69)(17,71)(18,73)(19,72)(20,74)(21,64)(22,63)(23,65)
(24,67)(25,66)(26,68)(27,88)(28,87)(29,89)(30,91)(31,90)(32,92)(33,97)(34,96)
(35,98)(36,94)(37,93)(38,95)(39,76)(40,75)(41,77)(42,79)(43,78)(44,80)(45,85)
(46,84)(47,86)(48,82)(49,81)(50,83);;
s3 := ( 99,100);;
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, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(100)!(1,2);
s1 := Sym(100)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,21)(16,23)(17,22)(18,24)
(19,26)(20,25)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)
(36,45)(37,47)(38,46)(51,75)(52,77)(53,76)(54,78)(55,80)(56,79)(57,84)(58,86)
(59,85)(60,81)(61,83)(62,82)(63,93)(64,95)(65,94)(66,96)(67,98)(68,97)(69,87)
(70,89)(71,88)(72,90)(73,92)(74,91);
s2 := Sym(100)!( 3,52)( 4,51)( 5,53)( 6,55)( 7,54)( 8,56)( 9,61)(10,60)(11,62)
(12,58)(13,57)(14,59)(15,70)(16,69)(17,71)(18,73)(19,72)(20,74)(21,64)(22,63)
(23,65)(24,67)(25,66)(26,68)(27,88)(28,87)(29,89)(30,91)(31,90)(32,92)(33,97)
(34,96)(35,98)(36,94)(37,93)(38,95)(39,76)(40,75)(41,77)(42,79)(43,78)(44,80)
(45,85)(46,84)(47,86)(48,82)(49,81)(50,83);
s3 := Sym(100)!( 99,100);
poly := sub<Sym(100)|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, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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