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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,2}*432
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 5
Schlafli Type : {2,6,6,2}
Number of vertices, edges, etc : 2, 9, 27, 9, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2,2} of size 864
   {2,6,6,2,3} of size 1296
   {2,6,6,2,4} of size 1728
Vertex Figure Of :
   {2,2,6,6,2} of size 864
   {3,2,6,6,2} of size 1296
   {4,2,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,6,2}*864b
   3-fold covers : {2,6,18,2}*1296a, {2,18,6,2}*1296a, {2,6,6,2}*1296a, {2,6,6,2}*1296b, {2,6,18,2}*1296b, {2,18,6,2}*1296b, {2,6,18,2}*1296c, {2,18,6,2}*1296c, {2,6,6,6}*1296b, {6,6,6,2}*1296a
   4-fold covers : {2,6,12,2}*1728b, {2,12,6,2}*1728b, {2,6,6,4}*1728b, {4,6,6,2}*1728b, {2,6,6,4}*1728d, {2,6,12,2}*1728d, {2,12,6,2}*1728d, {4,6,6,2}*1728g
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope