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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,2,2,3}*288
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 6
Schlafli Type : {2,6,2,2,3}
Number of vertices, edges, etc : 2, 6, 6, 2, 3, 3
Order of s₀s₁s₂s₃s₄s₅ : 6
Order of s₀s₁s₂s₃s₄s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,2,2,3,2} of size 576
   {2,6,2,2,3,3} of size 1152
   {2,6,2,2,3,4} of size 1152
   {2,6,2,2,3,6} of size 1728
Vertex Figure Of :
   {2,2,6,2,2,3} of size 576
   {3,2,6,2,2,3} of size 864
   {4,2,6,2,2,3} of size 1152
   {5,2,6,2,2,3} of size 1440
   {6,2,6,2,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,2,2,3}*144
   3-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,2,2,3}*576, {2,6,4,2,3}*576a, {4,6,2,2,3}*576a, {2,6,2,2,6}*576
   3-fold covers : {2,6,2,2,9}*864, {2,18,2,2,3}*864, {2,6,2,6,3}*864, {2,6,6,2,3}*864a, {2,6,6,2,3}*864c, {6,6,2,2,3}*864a, {6,6,2,2,3}*864b
   4-fold covers : {2,12,4,2,3}*1152a, {4,12,2,2,3}*1152a, {4,6,4,2,3}*1152a, {2,6,8,2,3}*1152, {8,6,2,2,3}*1152, {2,24,2,2,3}*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, {2,6,2,4,3}*1152, {2,6,4,2,3}*1152, {4,6,2,2,3}*1152
   5-fold covers : {2,6,10,2,3}*1440, {10,6,2,2,3}*1440, {2,6,2,2,15}*1440, {2,30,2,2,3}*1440
   6-fold covers : {2,12,2,2,9}*1728, {2,36,2,2,3}*1728, {2,6,4,2,9}*1728a, {2,18,4,2,3}*1728a, {4,6,2,2,9}*1728a, {4,18,2,2,3}*1728a, {2,6,2,2,18}*1728, {2,18,2,2,6}*1728, {2,6,12,2,3}*1728a, {2,12,2,6,3}*1728, {2,12,6,2,3}*1728a, {2,12,6,2,3}*1728b, {6,12,2,2,3}*1728a, {6,12,2,2,3}*1728b, {12,6,2,2,3}*1728a, {4,6,2,6,3}*1728a, {4,6,6,2,3}*1728a, {4,6,6,2,3}*1728b, {6,6,4,2,3}*1728a, {6,6,4,2,3}*1728b, {2,6,4,6,3}*1728, {2,6,12,2,3}*1728c, {12,6,2,2,3}*1728c, {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 := (5,6)(7,8);;
s2 := (3,7)(4,5)(6,8);;
s3 := ( 9,10);;
s4 := (12,13);;
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*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, s4*s5*s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope