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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2,2}*432
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 5
Schlafli Type : {6,6,2,2}
Number of vertices, edges, etc : 9, 27, 9, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2,2} of size 864
   {6,6,2,2,3} of size 1296
   {6,6,2,2,4} of size 1728
Vertex Figure Of :
   {2,6,6,2,2} of size 864
   {4,6,6,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,6,2,4}*864, {6,6,2,2}*864b
   3-fold covers : {6,18,2,2}*1296a, {18,6,2,2}*1296a, {6,6,2,2}*1296a, {6,6,2,2}*1296b, {6,18,2,2}*1296b, {18,6,2,2}*1296b, {6,18,2,2}*1296c, {18,6,2,2}*1296c, {6,6,2,6}*1296, {6,6,6,2}*1296b
   4-fold covers : {6,6,2,8}*1728, {6,12,2,2}*1728b, {12,6,2,2}*1728b, {6,6,2,4}*1728b, {6,6,4,2}*1728b, {6,6,4,2}*1728d, {6,12,2,2}*1728d, {12,6,2,2}*1728d
Permutation Representation (GAP) :
s0 := (4,5)(6,7)(8,9);;
s1 := (2,6)(3,4)(5,7);;
s2 := (1,2)(4,9)(5,8)(6,7);;
s3 := (10,11);;
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*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*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(4,5)(6,7)(8,9);
s1 := Sym(13)!(2,6)(3,4)(5,7);
s2 := Sym(13)!(1,2)(4,9)(5,8)(6,7);
s3 := Sym(13)!(10,11);
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*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*s1*s2*s0*s1*s2*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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