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

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

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