Polytope of Type {6,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,3}*1296
if this polytope has a name.
Group : SmallGroup(1296,3490)
Rank : 4
Schlafli Type : {6,6,3}
Number of vertices, edges, etc : 27, 108, 54, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 6
Special Properties :
   Non-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, 3)( 5, 6)( 8, 9)(11,12);;
s1 := ( 1, 2)( 4,11)( 5,12)( 6,10)( 7, 9);;
s2 := ( 7,10)( 8,11)( 9,12);;
s3 := (1,7)(2,9)(3,8);;
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*s2*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s3*s2*s1*s0*s1*s2*s3*s1*s2*s1*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!( 2, 3)( 5, 6)( 8, 9)(11,12);
s1 := Sym(12)!( 1, 2)( 4,11)( 5,12)( 6,10)( 7, 9);
s2 := Sym(12)!( 7,10)( 8,11)( 9,12);
s3 := Sym(12)!(1,7)(2,9)(3,8);
poly := sub<Sym(12)|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*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s3*s2*s1*s0*s1*s2*s3*s1*s2*s1*s0*s1, 
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0 >;

References : None.
to this polytope