Polytope of Type {12,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3,2}*1152
if this polytope has a name.
Group : SmallGroup(1152,157851)
Rank : 4
Schlafli Type : {12,3,2}
Number of vertices, edges, etc : 96, 144, 24, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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) :
   4-fold quotients : {6,3,2}*288, {12,3,2}*288
   12-fold quotients : {4,3,2}*96, {6,3,2}*96
   16-fold quotients : {6,3,2}*72
   24-fold quotients : {3,3,2}*48, {4,3,2}*48
   48-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope