Polytope of Type {9,2,3,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,3,6}*648
if this polytope has a name.
Group : SmallGroup(648,554)
Rank : 5
Schlafli Type : {9,2,3,6}
Number of vertices, edges, etc : 9, 9, 3, 9, 6
Order of s₀s₁s₂s₃s₄ : 18
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,3,6,2} of size 1296
   {9,2,3,6,3} of size 1944
Vertex Figure Of :
   {2,9,2,3,6} of size 1296
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {9,2,3,2}*216, {3,2,3,6}*216
   9-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,6,6}*1296c, {18,2,3,6}*1296
   3-fold covers : {9,2,9,6}*1944, {9,6,3,6}*1944, {9,2,3,6}*1944, {27,2,3,6}*1944
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7)(8,9);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (11,12)(13,14)(15,18)(16,17);;
s3 := (10,15)(11,13)(12,17)(14,16);;
s4 := (13,14)(15,16)(17,18);;
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, 
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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

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