Polytope of Type {2,8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,8}*1568b
if this polytope has a name.
Group : SmallGroup(1568,917)
Rank : 4
Schlafli Type : {2,8,8}
Number of vertices, edges, etc : 2, 49, 196, 49
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 := (1,2);;
s1 := ( 4,34)( 5,16)( 6,40)( 7,22)( 8,46)( 9,28)(10,36)(12,42)(13,17)(14,48)
(15,30)(18,44)(20,50)(21,25)(23,31)(24,39)(26,45)(29,33)(32,47)(37,41)
(38,49);;
s2 := ( 4,48)( 5,44)( 6,33)( 7,29)( 8,18)( 9,14)(10,32)(11,28)(12,17)(15,47)
(16,43)(19,46)(20,42)(21,31)(22,27)(24,41)(25,37)(30,45)(34,51)(35,40)
(38,50);;
s3 := ( 3,11)( 4,36)( 6,30)( 7,48)( 8,17)( 9,42)(10,34)(12,28)(13,46)(14,22)
(15,40)(18,26)(19,51)(21,38)(23,32)(25,49)(27,43)(29,37)(31,47)(33,41)
(44,45);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s1*s2*s3*s2*s3*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope