Polytope of Type {4,3,2,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2,6,2}*576
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 6
Schlafli Type : {4,3,2,6,2}
Number of vertices, edges, etc : 4, 6, 3, 6, 6, 2
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,2,6,2,2} of size 1152
   {4,3,2,6,2,3} of size 1728
Vertex Figure Of :
   {2,4,3,2,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,3,2,3,2}*288
   3-fold quotients : {4,3,2,2,2}*192
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,2,12,2}*1152, {4,3,2,6,4}*1152a, {4,3,2,6,2}*1152, {4,6,2,6,2}*1152b, {4,6,2,6,2}*1152c
   3-fold covers : {4,3,2,18,2}*1728, {4,9,2,6,2}*1728, {4,3,6,6,2}*1728a, {4,3,2,6,6}*1728a, {4,3,2,6,6}*1728c, {4,3,6,6,2}*1728b
Permutation Representation (GAP) :

s0 := (1,2)(3,4);;
s1 := (2,3);;
s2 := (3,4);;
s3 := ( 7, 8)( 9,10);;
s4 := ( 5, 9)( 6, 7)( 8,10);;
s5 := (11,12);;
poly := Group([s0,s1,s2,s3,s4,s5]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(1,2)(3,4);
s1 := Sym(12)!(2,3);
s2 := Sym(12)!(3,4);
s3 := Sym(12)!( 7, 8)( 9,10);
s4 := Sym(12)!( 5, 9)( 6, 7)( 8,10);
s5 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope