Polytope of Type {2,22,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,8}*704
if this polytope has a name.
Group : SmallGroup(704,1204)
Rank : 4
Schlafli Type : {2,22,8}
Number of vertices, edges, etc : 2, 22, 88, 8
Order of s₀s₁s₂s₃ : 88
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,22,8,2} of size 1408
Vertex Figure Of :
   {2,2,22,8} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,22,4}*352
   4-fold quotients : {2,22,2}*176
   8-fold quotients : {2,11,2}*88
   11-fold quotients : {2,2,8}*64
   22-fold quotients : {2,2,4}*32
   44-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,44,8}*1408a, {4,22,8}*1408, {2,22,16}*1408
Permutation Representation (GAP) :

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

to this polytope