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Polytope of Type {2,4,46}

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

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