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Polytope of Type {6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,2}*288d
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {6,12,2}
Number of vertices, edges, etc : 6, 36, 12, 2
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,12,2,2} of size 576
   {6,12,2,3} of size 864
   {6,12,2,4} of size 1152
   {6,12,2,5} of size 1440
   {6,12,2,6} of size 1728
Vertex Figure Of :
   {2,6,12,2} of size 576
   {4,6,12,2} of size 1152
   {6,6,12,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,4,2}*96b
   6-fold quotients : {3,4,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12,2}*576a
   3-fold covers : {6,36,2}*864c, {18,12,2}*864c, {6,12,2}*864d, {6,12,6}*864i
   4-fold covers : {6,24,2}*1152a, {6,12,4}*1152d, {12,12,2}*1152d, {6,12,2}*1152b, {6,12,4}*1152i, {6,24,2}*1152c, {6,24,2}*1152e, {12,12,2}*1152j, {6,12,4}*1152k, {12,12,2}*1152l
   5-fold covers : {30,12,2}*1440d, {6,60,2}*1440d
   6-fold covers : {6,36,2}*1728, {18,12,2}*1728a, {6,12,2}*1728b, {6,12,6}*1728i, {6,12,6}*1728k, {6,12,2}*1728c
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)(11,12);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s2 := ( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,10)(11,12);;
s3 := (13,14);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s0*s1*s2*s0*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(14)!( 3, 4)( 7, 8)(11,12);
s1 := Sym(14)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);
s2 := Sym(14)!( 1, 6)( 2, 5)( 3, 8)( 4, 7)( 9,10)(11,12);
s3 := Sym(14)!(13,14);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 

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