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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,2,3}*288a
if this polytope has a name.
Group : SmallGroup(288,958)
Rank : 5
Schlafli Type : {6,4,2,3}
Number of vertices, edges, etc : 6, 12, 4, 3, 3
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,4,2,3,2} of size 576
   {6,4,2,3,3} of size 1152
   {6,4,2,3,4} of size 1152
   {6,4,2,3,6} of size 1728
Vertex Figure Of :
   {2,6,4,2,3} of size 576
   {3,6,4,2,3} of size 864
   {4,6,4,2,3} of size 1152
   {3,6,4,2,3} of size 1152
   {4,6,4,2,3} of size 1152
   {6,6,4,2,3} of size 1728
   {6,6,4,2,3} of size 1728
   {6,6,4,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,2,2,3}*144
   3-fold quotients : {2,4,2,3}*96
   4-fold quotients : {3,2,2,3}*72
   6-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,4,2,3}*576a, {6,8,2,3}*576, {6,4,2,6}*576a
   3-fold covers : {6,4,2,9}*864a, {18,4,2,3}*864a, {6,12,2,3}*864a, {6,4,6,3}*864, {6,12,2,3}*864c
   4-fold covers : {12,8,2,3}*1152a, {24,4,2,3}*1152a, {12,8,2,3}*1152b, {24,4,2,3}*1152b, {12,4,2,3}*1152a, {6,16,2,3}*1152, {6,4,4,6}*1152, {12,4,2,6}*1152a, {6,4,2,12}*1152a, {6,8,2,6}*1152, {6,4,4,3}*1152b, {6,4,2,3}*1152b
   5-fold covers : {6,20,2,3}*1440a, {6,4,2,15}*1440a, {30,4,2,3}*1440a
   6-fold covers : {12,4,2,9}*1728a, {36,4,2,3}*1728a, {6,8,2,9}*1728, {18,8,2,3}*1728, {6,4,2,18}*1728a, {18,4,2,6}*1728a, {6,24,2,3}*1728a, {12,12,2,3}*1728a, {12,12,2,3}*1728c, {12,4,6,3}*1728, {6,8,6,3}*1728, {6,24,2,3}*1728c, {6,12,2,6}*1728a, {6,4,6,6}*1728a, {6,4,6,6}*1728c, {6,12,2,6}*1728c
Permutation Representation (GAP) :
s0 := ( 3, 4)( 6, 7)( 9,10)(11,12);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);;
s3 := (14,15);;
s4 := (13,14);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(15)!( 3, 4)( 6, 7)( 9,10)(11,12);
s1 := Sym(15)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,11);
s2 := Sym(15)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,11)(10,12);
s3 := Sym(15)!(14,15);
s4 := Sym(15)!(13,14);
poly := sub<Sym(15)|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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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