Polytope of Type {8,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8,2}*1568b
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 4
Schlafli Type : {8,8,2}
Number of vertices, edges, etc : 49, 196, 49, 2
Order of s₀s₁s₂s₃ : 14
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2,32)( 3,14)( 4,38)( 5,20)( 6,44)( 7,26)( 8,34)(10,40)(11,15)(12,46)
(13,28)(16,42)(18,48)(19,23)(21,29)(22,37)(24,43)(27,31)(30,45)(35,39)
(36,47);;
s1 := ( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)(13,45)
(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)
(36,48);;
s2 := ( 1, 9)( 2,34)( 4,28)( 5,46)( 6,15)( 7,40)( 8,32)(10,26)(11,44)(12,20)
(13,38)(16,24)(17,49)(19,36)(21,30)(23,47)(25,41)(27,35)(29,45)(31,39)
(42,43);;
s3 := (50,51);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(51)!( 2,32)( 3,14)( 4,38)( 5,20)( 6,44)( 7,26)( 8,34)(10,40)(11,15)
(12,46)(13,28)(16,42)(18,48)(19,23)(21,29)(22,37)(24,43)(27,31)(30,45)(35,39)
(36,47);
s1 := Sym(51)!( 2,46)( 3,42)( 4,31)( 5,27)( 6,16)( 7,12)( 8,30)( 9,26)(10,15)
(13,45)(14,41)(17,44)(18,40)(19,29)(20,25)(22,39)(23,35)(28,43)(32,49)(33,38)
(36,48);
s2 := Sym(51)!( 1, 9)( 2,34)( 4,28)( 5,46)( 6,15)( 7,40)( 8,32)(10,26)(11,44)
(12,20)(13,38)(16,24)(17,49)(19,36)(21,30)(23,47)(25,41)(27,35)(29,45)(31,39)
(42,43);
s3 := Sym(51)!(50,51);
poly := sub<Sym(51)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;

to this polytope