Polytope of Type {2,2,4,44}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,44}*1408
if this polytope has a name.
Group : SmallGroup(1408,17727)
Rank : 5
Schlafli Type : {2,2,4,44}
Number of vertices, edges, etc : 2, 2, 4, 88, 44
Order of s₀s₁s₂s₃s₄ : 44
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 : {2,2,2,44}*704, {2,2,4,22}*704
   4-fold quotients : {2,2,2,22}*352
   8-fold quotients : {2,2,2,11}*176
   11-fold quotients : {2,2,4,4}*128
   22-fold quotients : {2,2,2,4}*64, {2,2,4,2}*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 := (49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)(58,69)
(59,70)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)(80,91)
(81,92);;
s3 := ( 5,49)( 6,59)( 7,58)( 8,57)( 9,56)(10,55)(11,54)(12,53)(13,52)(14,51)
(15,50)(16,60)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)
(26,61)(27,71)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)
(37,72)(38,82)(39,92)(40,91)(41,90)(42,89)(43,88)(44,87)(45,86)(46,85)(47,84)
(48,83);;
s4 := ( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)(21,23)
(27,28)(29,37)(30,36)(31,35)(32,34)(38,39)(40,48)(41,47)(42,46)(43,45)(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);;
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(92)!(1,2);
s1 := Sym(92)!(3,4);
s2 := Sym(92)!(49,60)(50,61)(51,62)(52,63)(53,64)(54,65)(55,66)(56,67)(57,68)
(58,69)(59,70)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)
(80,91)(81,92);
s3 := Sym(92)!( 5,49)( 6,59)( 7,58)( 8,57)( 9,56)(10,55)(11,54)(12,53)(13,52)
(14,51)(15,50)(16,60)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)
(25,62)(26,61)(27,71)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)
(36,73)(37,72)(38,82)(39,92)(40,91)(41,90)(42,89)(43,88)(44,87)(45,86)(46,85)
(47,84)(48,83);
s4 := Sym(92)!( 5, 6)( 7,15)( 8,14)( 9,13)(10,12)(16,17)(18,26)(19,25)(20,24)
(21,23)(27,28)(29,37)(30,36)(31,35)(32,34)(38,39)(40,48)(41,47)(42,46)(43,45)
(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);
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*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 >;

to this polytope