Polytope of Type {9,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6,2}*648b
if this polytope has a name.
Group : SmallGroup(648,299)
Rank : 4
Schlafli Type : {9,6,2}
Number of vertices, edges, etc : 27, 81, 18, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,6,2,2} of size 1296
   {9,6,2,3} of size 1944
Vertex Figure Of :
   {2,9,6,2} of size 1296
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,6,2}*216
   9-fold quotients : {3,6,2}*72
   27-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,6,4}*1296c, {18,6,2}*1296d
   3-fold covers : {9,6,2}*1944a, {9,6,2}*1944b, {9,6,2}*1944c, {9,6,2}*1944d, {9,18,2}*1944j, {9,6,6}*1944g
Permutation Representation (GAP) :

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

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