Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*720c
if this polytope has a name.
Group : SmallGroup(720,767)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 60, 180, 60
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 1440
Vertex Figure Of :
   {2,6,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,6}*240b
   6-fold quotients : {6,6}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,6}*1440a, {12,6}*1440b, {6,6}*1440d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope