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Polytope of Type {2,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,3}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {2,6,3}
Number of vertices, edges, etc : 2, 24, 36, 12
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,3,2} of size 576
   {2,6,3,4} of size 1152
   {2,6,3,3} of size 1440
   {2,6,3,6} of size 1728
Vertex Figure Of :
   {2,2,6,3} of size 576
   {3,2,6,3} of size 864
   {4,2,6,3} of size 1152
   {5,2,6,3} of size 1440
   {6,2,6,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,6,3}*96
   4-fold quotients : {2,6,3}*72
   6-fold quotients : {2,3,3}*48
   12-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,12,3}*576, {4,6,3}*576a, {2,6,6}*576a
   3-fold covers : {2,6,9}*864, {2,6,3}*864, {6,6,3}*864
   4-fold covers : {2,6,3}*1152, {4,6,3}*1152a, {8,6,3}*1152, {4,12,3}*1152b, {2,6,12}*1152a, {2,12,6}*1152c, {2,6,6}*1152a, {2,6,12}*1152d, {4,6,6}*1152f, {2,12,6}*1152e, {2,12,3}*1152
   5-fold covers : {10,6,3}*1440, {2,6,15}*1440e
   6-fold covers : {2,12,9}*1728, {4,6,9}*1728a, {2,12,3}*1728, {4,6,3}*1728a, {2,6,18}*1728, {2,6,6}*1728b, {6,12,3}*1728, {12,6,3}*1728, {6,6,6}*1728a, {2,6,6}*1728c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 6)( 9,10)(13,14);;
s2 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14);;
s3 := ( 3, 8)( 4, 7)( 5, 9)( 6,10)(11,12);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!(1,2);
s1 := Sym(14)!( 5, 6)( 9,10)(13,14);
s2 := Sym(14)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14);
s3 := Sym(14)!( 3, 8)( 4, 7)( 5, 9)( 6,10)(11,12);
poly := sub<Sym(14)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >; 
 

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