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Polytope of Type {2,2,22,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,22,8}*1408
if this polytope has a name.
Group : SmallGroup(1408,19224)
Rank : 5
Schlafli Type : {2,2,22,8}
Number of vertices, edges, etc : 2, 2, 22, 88, 8
Order of s0s1s2s3s4 : 88
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 : {2,2,22,4}*704
   4-fold quotients : {2,2,22,2}*352
   8-fold quotients : {2,2,11,2}*176
   11-fold quotients : {2,2,2,8}*128
   22-fold quotients : {2,2,2,4}*64
   44-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 := ( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)(21,22)
(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)(50,59)
(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66)(72,81)(73,80)
(74,79)(75,78)(76,77)(83,92)(84,91)(85,90)(86,89)(87,88);;
s3 := ( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)(21,23)
(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)
(49,72)(50,71)(51,81)(52,80)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)(59,73)
(60,83)(61,82)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)
(70,84);;
s4 := ( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,58)
(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)(25,69)
(26,70)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)(36,91)
(37,92)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)(47,80)
(48,81);;
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*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(92)!(1,2);
s1 := Sym(92)!(3,4);
s2 := Sym(92)!( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(17,26)(18,25)(19,24)(20,23)
(21,22)(28,37)(29,36)(30,35)(31,34)(32,33)(39,48)(40,47)(41,46)(42,45)(43,44)
(50,59)(51,58)(52,57)(53,56)(54,55)(61,70)(62,69)(63,68)(64,67)(65,66)(72,81)
(73,80)(74,79)(75,78)(76,77)(83,92)(84,91)(85,90)(86,89)(87,88);
s3 := Sym(92)!( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)
(21,23)(27,39)(28,38)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)
(37,40)(49,72)(50,71)(51,81)(52,80)(53,79)(54,78)(55,77)(56,76)(57,75)(58,74)
(59,73)(60,83)(61,82)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)
(70,84);
s4 := Sym(92)!( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)
(14,58)(15,59)(16,60)(17,61)(18,62)(19,63)(20,64)(21,65)(22,66)(23,67)(24,68)
(25,69)(26,70)(27,82)(28,83)(29,84)(30,85)(31,86)(32,87)(33,88)(34,89)(35,90)
(36,91)(37,92)(38,71)(39,72)(40,73)(41,74)(42,75)(43,76)(44,77)(45,78)(46,79)
(47,80)(48,81);
poly := sub<Sym(92)|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*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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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