Polytope of Type {5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5}*660
Also Known As : {5,5}₅. if this polytope has another name.
Group : SmallGroup(660,13)
Rank : 3
Schlafli Type : {5,5}
Number of vertices, edges, etc : 66, 165, 66
Order of s₀s₁s₂ : 5
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Dual
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {5,5,2} of size 1320
Vertex Figure Of :
   {2,5,5} of size 1320
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,5}*1320b, {5,10}*1320c, {5,10}*1320d, {10,5}*1320c, {10,5}*1320d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope