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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6}*288
if this polytope has a name.
Group : SmallGroup(288,1031)
Rank : 5
Schlafli Type : {2,2,4,6}
Number of vertices, edges, etc : 2, 2, 6, 18, 9
Order of s₀s₁s₂s₃s₄ : 4
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,4,6,2} of size 576
Vertex Figure Of :
   {2,2,2,4,6} of size 576
   {3,2,2,4,6} of size 864
   {4,2,2,4,6} of size 1152
   {5,2,2,4,6} of size 1440
   {6,2,2,4,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,4,6}*576, {2,4,4,6}*576, {2,2,4,6}*576
   3-fold covers : {2,2,4,6}*864, {2,2,12,6}*864a, {2,2,12,6}*864b, {2,6,4,6}*864b, {6,2,4,6}*864, {2,2,12,6}*864c
   4-fold covers : {4,4,4,6}*1152, {2,8,4,6}*1152, {8,2,4,6}*1152, {2,2,4,12}*1152, {2,4,4,6}*1152, {4,2,4,6}*1152, {2,2,8,6}*1152
   5-fold covers : {2,10,4,6}*1440, {10,2,4,6}*1440, {2,2,20,6}*1440
   6-fold covers : {4,2,4,6}*1728, {4,2,12,6}*1728a, {4,2,12,6}*1728b, {2,4,4,6}*1728a, {2,4,12,6}*1728a, {2,4,12,6}*1728b, {2,2,4,6}*1728a, {2,2,12,6}*1728e, {2,2,12,6}*1728f, {12,2,4,6}*1728, {2,12,4,6}*1728, {6,4,4,6}*1728a, {4,6,4,6}*1728a, {4,2,12,6}*1728c, {2,4,12,6}*1728c, {2,2,4,6}*1728b, {2,2,12,6}*1728h, {2,6,4,6}*1728a, {6,2,4,6}*1728, {2,2,12,6}*1728i
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope