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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,3,2,2}*288
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 7
Schlafli Type : {3,2,2,3,2,2}
Number of vertices, edges, etc : 3, 3, 2, 3, 3, 2, 2
Order of s₀s₁s₂s₃s₄s₅s₆ : 6
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,3,2,2,2} of size 576
   {3,2,2,3,2,2,3} of size 864
   {3,2,2,3,2,2,4} of size 1152
   {3,2,2,3,2,2,5} of size 1440
   {3,2,2,3,2,2,6} of size 1728
Vertex Figure Of :
   {2,3,2,2,3,2,2} of size 576
   {3,3,2,2,3,2,2} of size 1152
   {4,3,2,2,3,2,2} of size 1152
   {6,3,2,2,3,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,3,2,4}*576, {3,2,2,6,2,2}*576, {6,2,2,3,2,2}*576
   3-fold covers : {3,2,2,9,2,2}*864, {9,2,2,3,2,2}*864, {3,2,2,3,2,6}*864, {3,2,2,3,6,2}*864, {3,2,6,3,2,2}*864, {3,6,2,3,2,2}*864
   4-fold covers : {3,2,2,3,2,8}*1152, {3,2,2,6,2,4}*1152, {3,2,2,6,4,2}*1152a, {3,2,4,6,2,2}*1152a, {6,2,2,3,2,4}*1152, {6,4,2,3,2,2}*1152a, {3,2,2,12,2,2}*1152, {12,2,2,3,2,2}*1152, {6,2,2,6,2,2}*1152, {3,2,2,3,4,2}*1152, {3,2,4,3,2,2}*1152, {3,4,2,3,2,2}*1152
   5-fold covers : {3,2,2,3,2,10}*1440, {3,2,2,15,2,2}*1440, {15,2,2,3,2,2}*1440
   6-fold covers : {3,2,2,9,2,4}*1728, {9,2,2,3,2,4}*1728, {3,2,2,18,2,2}*1728, {6,2,2,9,2,2}*1728, {9,2,2,6,2,2}*1728, {18,2,2,3,2,2}*1728, {3,2,2,3,2,12}*1728, {3,2,6,3,2,4}*1728, {3,6,2,3,2,4}*1728, {3,2,2,3,6,4}*1728, {3,2,2,6,2,6}*1728, {3,2,2,6,6,2}*1728a, {3,2,2,6,6,2}*1728c, {3,2,6,6,2,2}*1728a, {3,2,6,6,2,2}*1728b, {3,6,2,6,2,2}*1728, {6,2,2,3,2,6}*1728, {6,2,2,3,6,2}*1728, {6,2,6,3,2,2}*1728, {6,6,2,3,2,2}*1728a, {6,6,2,3,2,2}*1728c
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := (7,8);;
s4 := (6,7);;
s5 := ( 9,10);;
s6 := (11,12);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s2*s0*s2, s1*s2*s1*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, s0*s6*s0*s6, s1*s6*s1*s6, 
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6, 
s5*s6*s5*s6, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!(2,3);
s1 := Sym(12)!(1,2);
s2 := Sym(12)!(4,5);
s3 := Sym(12)!(7,8);
s4 := Sym(12)!(6,7);
s5 := Sym(12)!( 9,10);
s6 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*s2, 
s1*s2*s1*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, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4 >;

to this polytope