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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,4,2}*288
if this polytope has a name.
Group : SmallGroup(288,1028)
Rank : 5
Schlafli Type : {6,3,4,2}
Number of vertices, edges, etc : 6, 9, 6, 4, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,3,4,2,2} of size 576
   {6,3,4,2,3} of size 864
   {6,3,4,2,4} of size 1152
   {6,3,4,2,5} of size 1440
   {6,3,4,2,6} of size 1728
Vertex Figure Of :
   {2,6,3,4,2} of size 576
   {3,6,3,4,2} of size 864
   {4,6,3,4,2} of size 1152
   {6,6,3,4,2} of size 1728
   {6,6,3,4,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,3,4,2}*576, {6,6,4,2}*576e, {6,6,4,2}*576f
   3-fold covers : {6,9,4,2}*864, {6,3,4,2}*864
   4-fold covers : {6,3,4,4}*1152a, {6,12,4,2}*1152f, {6,12,4,2}*1152g, {6,3,4,4}*1152b, {6,3,8,2}*1152, {12,6,4,2}*1152e, {6,3,4,2}*1152, {6,6,4,2}*1152b, {12,3,4,2}*1152
   5-fold covers : {6,15,4,2}*1440
   6-fold covers : {6,9,4,2}*1728, {6,18,4,2}*1728d, {6,18,4,2}*1728e, {6,3,4,2}*1728, {6,6,4,2}*1728e, {6,6,4,2}*1728f, {6,3,4,6}*1728, {6,3,12,2}*1728, {6,6,4,2}*1728i, {6,6,12,2}*1728h
Permutation Representation (GAP) :

s0 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s2 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s3*s2*s1*s3*s2*s1*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(14)!( 5, 9)( 6,10)( 7,11)( 8,12);
s1 := Sym(14)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);
s2 := Sym(14)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);
s3 := Sym(14)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s4 := Sym(14)!(13,14);
poly := sub<Sym(14)|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, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >;

to this polytope