Polytope of Type {2,2,2,2,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,2,2,9}*576
if this polytope has a name.
Group : SmallGroup(576,8267)
Rank : 7
Schlafli Type : {2,2,2,2,2,9}
Number of vertices, edges, etc : 2, 2, 2, 2, 2, 9, 9
Order of s₀s₁s₂s₃s₄s₅s₆ : 18
Order of s₀s₁s₂s₃s₄s₅s₆s₅s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,2,2,2,9,2} of size 1152
Vertex Figure Of :
   {2,2,2,2,2,2,9} of size 1152
   {3,2,2,2,2,2,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,2,2,2,2,3}*192
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,2,2,4,2,9}*1152, {2,2,4,2,2,9}*1152, {2,4,2,2,2,9}*1152, {4,2,2,2,2,9}*1152, {2,2,2,2,2,18}*1152
   3-fold covers : {2,2,2,2,2,27}*1728, {2,2,2,2,6,9}*1728, {2,2,2,6,2,9}*1728, {2,2,6,2,2,9}*1728, {2,6,2,2,2,9}*1728, {6,2,2,2,2,9}*1728
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := (7,8);;
s4 := ( 9,10);;
s5 := (12,13)(14,15)(16,17)(18,19);;
s6 := (11,12)(13,14)(15,16)(17,18);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  s6 := F.7;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
s6*s6, s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5, 
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6, 
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(19)!(1,2);
s1 := Sym(19)!(3,4);
s2 := Sym(19)!(5,6);
s3 := Sym(19)!(7,8);
s4 := Sym(19)!( 9,10);
s5 := Sym(19)!(12,13)(14,15)(16,17)(18,19);
s6 := Sym(19)!(11,12)(13,14)(15,16)(17,18);
poly := sub<Sym(19)|s0,s1,s2,s3,s4,s5,s6>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, s6*s6, s0*s1*s0*s1, 
s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5, s0*s6*s0*s6, 
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6, 
s4*s6*s4*s6, s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6*s5*s6 >;

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