Polytope of Type {2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,6}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 4
Schlafli Type : {2,3,6}
Number of vertices, edges, etc : 2, 12, 36, 24
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,6,2} of size 576
   {2,3,6,4} of size 1152
   {2,3,6,3} of size 1440
   {2,3,6,6} of size 1728
Vertex Figure Of :
   {2,2,3,6} of size 576
   {3,2,3,6} of size 864
   {4,2,3,6} of size 1152
   {5,2,3,6} of size 1440
   {6,2,3,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,6}*96
   4-fold quotients : {2,3,6}*72
   6-fold quotients : {2,3,3}*48
   12-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,12}*576, {2,6,6}*576b
   3-fold covers : {2,9,6}*864, {2,3,6}*864, {6,3,6}*864a
   4-fold covers : {2,3,6}*1152, {4,3,6}*1152a, {2,12,6}*1152a, {4,6,6}*1152c, {2,6,12}*1152c, {2,6,6}*1152b, {2,12,6}*1152d, {2,6,12}*1152e, {4,3,6}*1152b, {2,3,12}*1152
   5-fold covers : {2,15,6}*1440e
   6-fold covers : {2,9,12}*1728, {2,3,12}*1728, {2,18,6}*1728, {2,6,6}*1728a, {6,3,12}*1728, {6,6,6}*1728b, {6,6,6}*1728c, {2,6,6}*1728c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 7,11)( 8,12)( 9,14)(10,13);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13);;
s3 := ( 3, 4)( 7, 8)(11,12);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!(1,2);
s1 := Sym(14)!( 5, 6)( 7,11)( 8,12)( 9,14)(10,13);
s2 := Sym(14)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13);
s3 := Sym(14)!( 3, 4)( 7, 8)(11,12);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;

to this polytope