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Polytope of Type {4,44,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,44,2}*704
if this polytope has a name.
Group : SmallGroup(704,937)
Rank : 4
Schlafli Type : {4,44,2}
Number of vertices, edges, etc : 4, 88, 44, 2
Order of s0s1s2s3 : 44
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,44,2,2} of size 1408
Vertex Figure Of :
   {2,4,44,2} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,44,2}*352, {4,22,2}*352
   4-fold quotients : {2,22,2}*176
   8-fold quotients : {2,11,2}*88
   11-fold quotients : {4,4,2}*64
   22-fold quotients : {2,4,2}*32, {4,2,2}*32
   44-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,44,4}*1408, {8,44,2}*1408a, {4,88,2}*1408a, {8,44,2}*1408b, {4,88,2}*1408b, {4,44,2}*1408
Permutation Representation (GAP) :
s0 := (45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)
(55,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)
(77,88);;
s1 := ( 1,45)( 2,55)( 3,54)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)(10,47)
(11,46)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)(21,58)
(22,57)(23,67)(24,77)(25,76)(26,75)(27,74)(28,73)(29,72)(30,71)(31,70)(32,69)
(33,68)(34,78)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)
(44,79);;
s2 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)(17,19)
(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)(45,68)
(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)(56,79)
(57,78)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)(66,80);;
s3 := (89,90);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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(90)!(45,56)(46,57)(47,58)(48,59)(49,60)(50,61)(51,62)(52,63)(53,64)
(54,65)(55,66)(67,78)(68,79)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)
(76,87)(77,88);
s1 := Sym(90)!( 1,45)( 2,55)( 3,54)( 4,53)( 5,52)( 6,51)( 7,50)( 8,49)( 9,48)
(10,47)(11,46)(12,56)(13,66)(14,65)(15,64)(16,63)(17,62)(18,61)(19,60)(20,59)
(21,58)(22,57)(23,67)(24,77)(25,76)(26,75)(27,74)(28,73)(29,72)(30,71)(31,70)
(32,69)(33,68)(34,78)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)
(43,80)(44,79);
s2 := Sym(90)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,13)(14,22)(15,21)(16,20)
(17,19)(23,24)(25,33)(26,32)(27,31)(28,30)(34,35)(36,44)(37,43)(38,42)(39,41)
(45,68)(46,67)(47,77)(48,76)(49,75)(50,74)(51,73)(52,72)(53,71)(54,70)(55,69)
(56,79)(57,78)(58,88)(59,87)(60,86)(61,85)(62,84)(63,83)(64,82)(65,81)(66,80);
s3 := Sym(90)!(89,90);
poly := sub<Sym(90)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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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