Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*384a
if this polytope has a name.
Group : SmallGroup(384,5602)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 32, 96, 32
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 3
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 768
   {6,6,3} of size 1920
Vertex Figure Of :
   {2,6,6} of size 768
   {3,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*192a
   16-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*768a, {6,12}*768b, {12,6}*768a, {12,6}*768b, {6,6}*768e
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope