Polytope of Type {8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157849)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 144, 288, 72
Order of s0s1s2 : 6
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   16-fold quotients : {4,4}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14);;
s1 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,15)(10,16)(11,13)(12,14);
s1 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);
s2 := Sym(16)!( 2, 4)( 6, 8)(10,12)(14,16);
poly := sub<Sym(16)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*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*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope