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Polytope of Type {2,2,4,46}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,46}*1472
if this polytope has a name.
Group : SmallGroup(1472,1369)
Rank : 5
Schlafli Type : {2,2,4,46}
Number of vertices, edges, etc : 2, 2, 4, 92, 46
Order of s0s1s2s3s4 : 92
Order of s0s1s2s3s4s3s2s1 : 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 : {2,2,2,46}*736
   4-fold quotients : {2,2,2,23}*368
   23-fold quotients : {2,2,4,2}*64
   46-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (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)
(72,95)(73,96);;
s3 := ( 5,51)( 6,73)( 7,72)( 8,71)( 9,70)(10,69)(11,68)(12,67)(13,66)(14,65)
(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,56)(24,55)(25,54)
(26,53)(27,52)(28,74)(29,96)(30,95)(31,94)(32,93)(33,92)(34,91)(35,90)(36,89)
(37,88)(38,87)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81)(45,80)(46,79)(47,78)
(48,77)(49,76)(50,75);;
s4 := ( 5, 6)( 7,27)( 8,26)( 9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)
(16,18)(28,29)(30,50)(31,49)(32,48)(33,47)(34,46)(35,45)(36,44)(37,43)(38,42)
(39,41)(51,52)(53,73)(54,72)(55,71)(56,70)(57,69)(58,68)(59,67)(60,66)(61,65)
(62,64)(74,75)(76,96)(77,95)(78,94)(79,93)(80,92)(81,91)(82,90)(83,89)(84,88)
(85,87);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!(1,2);
s1 := Sym(96)!(3,4);
s2 := Sym(96)!(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)(72,95)(73,96);
s3 := Sym(96)!( 5,51)( 6,73)( 7,72)( 8,71)( 9,70)(10,69)(11,68)(12,67)(13,66)
(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)(22,57)(23,56)(24,55)
(25,54)(26,53)(27,52)(28,74)(29,96)(30,95)(31,94)(32,93)(33,92)(34,91)(35,90)
(36,89)(37,88)(38,87)(39,86)(40,85)(41,84)(42,83)(43,82)(44,81)(45,80)(46,79)
(47,78)(48,77)(49,76)(50,75);
s4 := Sym(96)!( 5, 6)( 7,27)( 8,26)( 9,25)(10,24)(11,23)(12,22)(13,21)(14,20)
(15,19)(16,18)(28,29)(30,50)(31,49)(32,48)(33,47)(34,46)(35,45)(36,44)(37,43)
(38,42)(39,41)(51,52)(53,73)(54,72)(55,71)(56,70)(57,69)(58,68)(59,67)(60,66)
(61,65)(62,64)(74,75)(76,96)(77,95)(78,94)(79,93)(80,92)(81,91)(82,90)(83,89)
(84,88)(85,87);
poly := sub<Sym(96)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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