Polytope of Type {3,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,6}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157478)
Rank : 4
Schlafli Type : {3,4,6}
Number of vertices, edges, etc : 12, 48, 96, 24
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 4
Special Properties :
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,3}*576
   32-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);;
s1 := ( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22);;
s2 := ( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);;
s3 := ( 1, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)(21,22)
(23,24);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s0*s2*s1*s0*s2*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(24)!( 5, 8)( 6, 7)(11,13)(12,14)(19,24)(20,23);
s1 := Sym(24)!( 3, 8)( 4, 7)(13,16)(14,15)(19,21)(20,22);
s2 := Sym(24)!( 3, 4)( 9,22)(10,21)(11,20)(12,19)(13,23)(14,24)(15,18)(16,17);
s3 := Sym(24)!( 1, 9)( 2,10)( 3,15)( 4,16)( 5,12)( 6,11)( 7,13)( 8,14)(19,20)
(21,22)(23,24);
poly := sub<Sym(24)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s0*s2*s1*s0*s2*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope