Polytope of Type {4,4,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,4}*1152d
if this polytope has a name.
Group : SmallGroup(1152,157849)
Rank : 4
Schlafli Type : {4,4,4}
Number of vertices, edges, etc : 9, 72, 72, 16
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Locally Toroidal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);;
s1 := ( 9,13)(10,14)(11,15)(12,16);;
s2 := ( 2,13)( 3, 9)( 4, 5)( 6,16)( 7,12)(10,15);;
s3 := ( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,14)(10,13)(11,16)(12,15);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s3*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(16)!( 2, 5)( 3, 9)( 4,13)( 7,10)( 8,14)(12,15);
s1 := Sym(16)!( 9,13)(10,14)(11,15)(12,16);
s2 := Sym(16)!( 2,13)( 3, 9)( 4, 5)( 6,16)( 7,12)(10,15);
s3 := Sym(16)!( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,14)(10,13)(11,16)(12,15);
poly := sub<Sym(16)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s3*s1*s2*s3*s2*s1*s0*s1*s2*s3*s2*s1 >;

References : None.
to this polytope