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Polytope of Type {3,4,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,6}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {3,4,2,6}
Number of vertices, edges, etc : 3, 6, 4, 6, 6
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,6,2} of size 576
   {3,4,2,6,3} of size 864
   {3,4,2,6,4} of size 1152
   {3,4,2,6,3} of size 1152
   {3,4,2,6,4} of size 1152
   {3,4,2,6,4} of size 1152
   {3,4,2,6,4} of size 1728
   {3,4,2,6,6} of size 1728
   {3,4,2,6,6} of size 1728
   {3,4,2,6,6} of size 1728
Vertex Figure Of :
   {2,3,4,2,6} of size 576
   {4,3,4,2,6} of size 1152
   {6,3,4,2,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,4,2,3}*144
   3-fold quotients : {3,4,2,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,2,12}*576, {3,4,2,6}*576, {6,4,2,6}*576b, {6,4,2,6}*576c
   3-fold covers : {3,4,2,18}*864, {9,4,2,6}*864
   4-fold covers : {3,4,4,6}*1152a, {3,4,2,24}*1152, {12,4,2,6}*1152b, {12,4,2,6}*1152c, {3,4,2,12}*1152, {6,4,2,12}*1152b, {6,4,2,12}*1152c, {3,4,4,6}*1152b, {3,8,2,6}*1152, {6,4,2,6}*1152
   5-fold covers : {15,4,2,6}*1440, {3,4,2,30}*1440
   6-fold covers : {3,4,2,36}*1728, {9,4,2,12}*1728, {3,4,2,18}*1728, {6,4,2,18}*1728b, {6,4,2,18}*1728c, {9,4,2,6}*1728, {18,4,2,6}*1728b, {18,4,2,6}*1728c, {3,4,6,6}*1728a, {3,4,6,6}*1728b, {3,12,2,6}*1728, {6,12,2,6}*1728d
Permutation Representation (GAP) :
s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := ( 7, 8)( 9,10);;
s4 := ( 5, 9)( 6, 7)( 8,10);;
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, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(3,4);
s1 := Sym(10)!(2,3);
s2 := Sym(10)!(1,2)(3,4);
s3 := Sym(10)!( 7, 8)( 9,10);
s4 := Sym(10)!( 5, 9)( 6, 7)( 8,10);
poly := sub<Sym(10)|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, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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