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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,8,22}*1408
if this polytope has a name.
Group : SmallGroup(1408,19224)
Rank : 5
Schlafli Type : {2,2,8,22}
Number of vertices, edges, etc : 2, 2, 8, 88, 22
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 : {2,2,4,22}*704
   4-fold quotients : {2,2,2,22}*352
   8-fold quotients : {2,2,2,11}*176
   11-fold quotients : {2,2,8,2}*128
   22-fold quotients : {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 := (27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)(36,47)
(37,48)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)(58,80)
(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(67,89)(68,90)(69,91)
(70,92);;
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)(27,82)(28,92)(29,91)(30,90)(31,89)(32,88)(33,87)(34,86)(35,85)(36,84)
(37,83)(38,71)(39,81)(40,80)(41,79)(42,78)(43,77)(44,76)(45,75)(46,74)(47,73)
(48,72);;
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)(49,50)
(51,59)(52,58)(53,57)(54,56)(60,61)(62,70)(63,69)(64,68)(65,67)(71,72)(73,81)
(74,80)(75,79)(76,78)(82,83)(84,92)(85,91)(86,90)(87,89);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(92)!(1,2);
s1 := Sym(92)!(3,4);
s2 := Sym(92)!(27,38)(28,39)(29,40)(30,41)(31,42)(32,43)(33,44)(34,45)(35,46)
(36,47)(37,48)(49,71)(50,72)(51,73)(52,74)(53,75)(54,76)(55,77)(56,78)(57,79)
(58,80)(59,81)(60,82)(61,83)(62,84)(63,85)(64,86)(65,87)(66,88)(67,89)(68,90)
(69,91)(70,92);
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)(27,82)(28,92)(29,91)(30,90)(31,89)(32,88)(33,87)(34,86)(35,85)
(36,84)(37,83)(38,71)(39,81)(40,80)(41,79)(42,78)(43,77)(44,76)(45,75)(46,74)
(47,73)(48,72);
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)
(49,50)(51,59)(52,58)(53,57)(54,56)(60,61)(62,70)(63,69)(64,68)(65,67)(71,72)
(73,81)(74,80)(75,79)(76,78)(82,83)(84,92)(85,91)(86,90)(87,89);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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 >;

to this polytope