Polytope of Type {4,4,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,4,6,2}*576
if this polytope has a name.
Group : SmallGroup(576,8418)
Rank : 5
Schlafli Type : {4,4,6,2}
Number of vertices, edges, etc : 4, 12, 18, 9, 2
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,4,6,2,2} of size 1152
   {4,4,6,2,3} of size 1728
Vertex Figure Of :
   {2,4,4,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,6,2}*288
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,4,6,2}*1152, {4,4,6,2}*1152
   3-fold covers : {4,4,6,2}*1728a, {4,12,6,2}*1728a, {4,12,6,2}*1728b, {12,4,6,2}*1728, {4,12,6,2}*1728c
Permutation Representation (GAP) :

s0 := ( 7,10)( 8,11)( 9,12);;
s1 := ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);;
s2 := ( 8, 9)(11,12);;
s3 := ( 1, 2)( 4, 5)( 7, 8)(10,11);;
s4 := (13,14);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!( 7,10)( 8,11)( 9,12);
s1 := Sym(14)!( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12);
s2 := Sym(14)!( 8, 9)(11,12);
s3 := Sym(14)!( 1, 2)( 4, 5)( 7, 8)(10,11);
s4 := Sym(14)!(13,14);
poly := sub<Sym(14)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1 >;

to this polytope