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

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

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