Polytope of Type {2,88,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,88,2}*704
if this polytope has a name.
Group : SmallGroup(704,1190)
Rank : 4
Schlafli Type : {2,88,2}
Number of vertices, edges, etc : 2, 88, 88, 2
Order of s₀s₁s₂s₃ : 88
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,88,2,2} of size 1408
Vertex Figure Of :
   {2,2,88,2} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,44,2}*352
   4-fold quotients : {2,22,2}*176
   8-fold quotients : {2,11,2}*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 : {2,88,4}*1408a, {4,88,2}*1408a, {2,176,2}*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)
(25,36)(26,46)(27,45)(28,44)(29,43)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)
(47,69)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)
(58,80)(59,90)(60,89)(61,88)(62,87)(63,86)(64,85)(65,84)(66,83)(67,82)
(68,81);;
s2 := ( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)(12,50)
(13,49)(14,59)(15,58)(16,68)(17,67)(18,66)(19,65)(20,64)(21,63)(22,62)(23,61)
(24,60)(25,81)(26,80)(27,90)(28,89)(29,88)(30,87)(31,86)(32,85)(33,84)(34,83)
(35,82)(36,70)(37,69)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)
(46,71);;
s3 := (91,92);;
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, 
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*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*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*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(92)!(1,2);
s1 := Sym(92)!( 4,13)( 5,12)( 6,11)( 7,10)( 8, 9)(15,24)(16,23)(17,22)(18,21)
(19,20)(25,36)(26,46)(27,45)(28,44)(29,43)(30,42)(31,41)(32,40)(33,39)(34,38)
(35,37)(47,69)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)
(57,70)(58,80)(59,90)(60,89)(61,88)(62,87)(63,86)(64,85)(65,84)(66,83)(67,82)
(68,81);
s2 := Sym(92)!( 3,48)( 4,47)( 5,57)( 6,56)( 7,55)( 8,54)( 9,53)(10,52)(11,51)
(12,50)(13,49)(14,59)(15,58)(16,68)(17,67)(18,66)(19,65)(20,64)(21,63)(22,62)
(23,61)(24,60)(25,81)(26,80)(27,90)(28,89)(29,88)(30,87)(31,86)(32,85)(33,84)
(34,83)(35,82)(36,70)(37,69)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)
(45,72)(46,71);
s3 := Sym(92)!(91,92);
poly := sub<Sym(92)|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, 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*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*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*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