Polytope of Type {2,8,22}

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

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

to this polytope