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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,2,2,6}*288
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 6
Schlafli Type : {2,3,2,2,6}
Number of vertices, edges, etc : 2, 3, 3, 2, 6, 6
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,2,2,6,2} of size 576
   {2,3,2,2,6,3} of size 864
   {2,3,2,2,6,4} of size 1152
   {2,3,2,2,6,3} of size 1152
   {2,3,2,2,6,4} of size 1152
   {2,3,2,2,6,4} of size 1152
   {2,3,2,2,6,4} of size 1728
   {2,3,2,2,6,6} of size 1728
   {2,3,2,2,6,6} of size 1728
   {2,3,2,2,6,6} of size 1728
Vertex Figure Of :
   {2,2,3,2,2,6} of size 576
   {3,2,3,2,2,6} of size 864
   {4,2,3,2,2,6} of size 1152
   {5,2,3,2,2,6} of size 1440
   {6,2,3,2,2,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,2,3}*144
   3-fold quotients : {2,3,2,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,2,2,12}*576, {2,3,2,4,6}*576a, {2,6,2,2,6}*576
   3-fold covers : {2,3,2,2,18}*864, {2,9,2,2,6}*864, {2,3,2,6,6}*864a, {2,3,2,6,6}*864b, {2,3,6,2,6}*864, {6,3,2,2,6}*864
   4-fold covers : {2,3,2,4,12}*1152a, {2,3,2,8,6}*1152, {2,3,2,2,24}*1152, {2,6,2,4,6}*1152a, {2,6,4,2,6}*1152a, {4,6,2,2,6}*1152a, {2,6,2,2,12}*1152, {2,12,2,2,6}*1152, {2,3,2,4,6}*1152, {2,3,4,2,6}*1152, {4,3,2,2,6}*1152
   5-fold covers : {2,3,2,10,6}*1440, {2,3,2,2,30}*1440, {2,15,2,2,6}*1440
   6-fold covers : {2,9,2,2,12}*1728, {2,3,2,2,36}*1728, {2,3,2,4,18}*1728a, {2,9,2,4,6}*1728a, {2,6,2,2,18}*1728, {2,18,2,2,6}*1728, {2,3,2,6,12}*1728a, {2,3,2,6,12}*1728b, {2,3,2,12,6}*1728a, {2,3,6,2,12}*1728, {6,3,2,2,12}*1728, {6,3,2,4,6}*1728a, {2,3,2,12,6}*1728c, {2,3,6,4,6}*1728, {2,6,2,6,6}*1728a, {2,6,2,6,6}*1728b, {2,6,6,2,6}*1728a, {2,6,6,2,6}*1728c, {6,6,2,2,6}*1728a, {6,6,2,2,6}*1728b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (4,5);;
s2 := (3,4);;
s3 := (6,7);;
s4 := (10,11)(12,13);;
s5 := ( 8,12)( 9,10)(11,13);;
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*s1*s0*s1, 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, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(13)!(1,2);
s1 := Sym(13)!(4,5);
s2 := Sym(13)!(3,4);
s3 := Sym(13)!(6,7);
s4 := Sym(13)!(10,11)(12,13);
s5 := Sym(13)!( 8,12)( 9,10)(11,13);
poly := sub<Sym(13)|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*s1*s0*s1, 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, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s1*s2*s1*s2*s1*s2, 
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;

to this polytope