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Polytope of Type {2,46,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,46,4}*736
if this polytope has a name.
Group : SmallGroup(736,177)
Rank : 4
Schlafli Type : {2,46,4}
Number of vertices, edges, etc : 2, 46, 92, 4
Order of s0s1s2s3 : 92
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,46,4,2} of size 1472
Vertex Figure Of :
   {2,2,46,4} of size 1472
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,46,2}*368
   4-fold quotients : {2,23,2}*184
   23-fold quotients : {2,2,4}*32
   46-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,92,4}*1472, {4,46,4}*1472, {2,46,8}*1472
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)(13,16)
(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)
(37,38)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)
(60,61)(73,94)(74,93)(75,92)(76,91)(77,90)(78,89)(79,88)(80,87)(81,86)(82,85)
(83,84);;
s2 := ( 3, 4)( 5,25)( 6,24)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)(13,17)
(14,16)(26,27)(28,48)(29,47)(30,46)(31,45)(32,44)(33,43)(34,42)(35,41)(36,40)
(37,39)(49,73)(50,72)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)
(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)
(70,75)(71,74);;
s3 := ( 3,49)( 4,50)( 5,51)( 6,52)( 7,53)( 8,54)( 9,55)(10,56)(11,57)(12,58)
(13,59)(14,60)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)(23,69)
(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,76)(31,77)(32,78)(33,79)(34,80)
(35,81)(36,82)(37,83)(38,84)(39,85)(40,86)(41,87)(42,88)(43,89)(44,90)(45,91)
(46,92)(47,93)(48,94);;
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*s3*s2*s1*s2*s3*s2, s2*s3*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(94)!(1,2);
s1 := Sym(94)!( 4,25)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)(11,18)(12,17)
(13,16)(14,15)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)
(36,39)(37,38)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)
(59,62)(60,61)(73,94)(74,93)(75,92)(76,91)(77,90)(78,89)(79,88)(80,87)(81,86)
(82,85)(83,84);
s2 := Sym(94)!( 3, 4)( 5,25)( 6,24)( 7,23)( 8,22)( 9,21)(10,20)(11,19)(12,18)
(13,17)(14,16)(26,27)(28,48)(29,47)(30,46)(31,45)(32,44)(33,43)(34,42)(35,41)
(36,40)(37,39)(49,73)(50,72)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)
(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)
(69,76)(70,75)(71,74);
s3 := Sym(94)!( 3,49)( 4,50)( 5,51)( 6,52)( 7,53)( 8,54)( 9,55)(10,56)(11,57)
(12,58)(13,59)(14,60)(15,61)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)
(23,69)(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,76)(31,77)(32,78)(33,79)
(34,80)(35,81)(36,82)(37,83)(38,84)(39,85)(40,86)(41,87)(42,88)(43,89)(44,90)
(45,91)(46,92)(47,93)(48,94);
poly := sub<Sym(94)|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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*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 >; 
 

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