Polytope of Type {3,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,4}*576b
if this polytope has a name.
Group : SmallGroup(576,8654)
Rank : 4
Schlafli Type : {3,6,4}
Number of vertices, edges, etc : 3, 36, 48, 16
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,4,2} of size 1152
Vertex Figure Of :
   {2,3,6,4} of size 1152
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,4}*1152c, {6,6,4}*1152i
   3-fold covers : {9,6,4}*1728b, {3,6,4}*1728b
Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s2 := ( 2, 3)( 7, 8)(10,12);;
s3 := ( 1, 4)( 2, 3)( 5, 7)( 6, 8)( 9,10)(11,12);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s1*s0*s1*s2*s3*s2*s1*s0*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope