Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*660
if this polytope has a name.
Group : SmallGroup(660,13)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 55, 165, 55
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 5
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 1320
Vertex Figure Of :
   {2,6,6} of size 1320
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6}*1320a, {6,6}*1320b, {6,6}*1320c, {6,6}*1320d, {6,6}*1320e, {6,6}*1320f, {6,6}*1320g
Permutation Representation (GAP) :

s0 := ( 3,11)( 4, 7)( 5, 6)( 8,10);;
s1 := ( 1, 2)( 5, 9)( 7,10)( 8,11);;
s2 := ( 2, 9)( 3,11)( 4, 6)( 5, 7);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*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, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*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, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope