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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,3,2,2}*288
if this polytope has a name.
Group : SmallGroup(288,1040)
Rank : 6
Schlafli Type : {6,2,3,2,2}
Number of vertices, edges, etc : 6, 6, 3, 3, 2, 2
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,2,3,2,2,2} of size 576
   {6,2,3,2,2,3} of size 864
   {6,2,3,2,2,4} of size 1152
   {6,2,3,2,2,5} of size 1440
   {6,2,3,2,2,6} of size 1728
Vertex Figure Of :
   {2,6,2,3,2,2} of size 576
   {3,6,2,3,2,2} of size 864
   {4,6,2,3,2,2} of size 1152
   {3,6,2,3,2,2} of size 1152
   {4,6,2,3,2,2} of size 1152
   {4,6,2,3,2,2} of size 1152
   {4,6,2,3,2,2} of size 1728
   {6,6,2,3,2,2} of size 1728
   {6,6,2,3,2,2} of size 1728
   {6,6,2,3,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,2,3,2,2}*144
   3-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,2,3,2,2}*576, {6,2,3,2,4}*576, {6,2,6,2,2}*576
   3-fold covers : {6,2,9,2,2}*864, {18,2,3,2,2}*864, {6,6,3,2,2}*864a, {6,2,3,2,6}*864, {6,2,3,6,2}*864, {6,6,3,2,2}*864b
   4-fold covers : {12,2,3,2,4}*1152, {6,2,3,2,8}*1152, {24,2,3,2,2}*1152, {6,2,6,2,4}*1152, {6,2,6,4,2}*1152a, {6,4,6,2,2}*1152, {6,2,12,2,2}*1152, {12,2,6,2,2}*1152, {6,2,3,4,2}*1152, {6,4,3,2,2}*1152
   5-fold covers : {6,2,3,2,10}*1440, {6,2,15,2,2}*1440, {30,2,3,2,2}*1440
   6-fold covers : {12,2,9,2,2}*1728, {36,2,3,2,2}*1728, {12,6,3,2,2}*1728a, {6,2,9,2,4}*1728, {18,2,3,2,4}*1728, {6,6,3,2,4}*1728a, {6,2,18,2,2}*1728, {18,2,6,2,2}*1728, {6,6,6,2,2}*1728a, {6,2,3,2,12}*1728, {12,2,3,2,6}*1728, {12,2,3,6,2}*1728, {6,6,3,2,4}*1728b, {12,6,3,2,2}*1728b, {6,2,3,6,4}*1728, {6,2,6,2,6}*1728, {6,2,6,6,2}*1728a, {6,2,6,6,2}*1728c, {6,6,6,2,2}*1728b, {6,6,6,2,2}*1728c, {6,6,6,2,2}*1728g
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (8,9);;
s3 := (7,8);;
s4 := (10,11);;
s5 := (12,13);;
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*s2*s0*s2, s1*s2*s1*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, s0*s5*s0*s5, 
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, 
s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(3,4)(5,6);
s1 := Sym(13)!(1,5)(2,3)(4,6);
s2 := Sym(13)!(8,9);
s3 := Sym(13)!(7,8);
s4 := Sym(13)!(10,11);
s5 := Sym(13)!(12,13);
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*s2*s0*s2, s1*s2*s1*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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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