Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1344f
if this polytope has a name.
Group : SmallGroup(1344,11295)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 84, 336, 56
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,8}*672i
   4-fold quotients : {6,8}*336b
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)(11,12);;
s1 := ( 2, 4)( 3, 6)( 5, 8)( 9,11)(10,12);;
s2 := ( 1, 4)( 2, 6)( 3, 5)( 7, 8)(11,12);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope