Polytope of Type {6,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,9}*324b
if this polytope has a name.
Group : SmallGroup(324,39)
Rank : 3
Schlafli Type : {6,9}
Number of vertices, edges, etc : 18, 81, 27
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,9,2} of size 648
   {6,9,4} of size 1296
   {6,9,6} of size 1944
Vertex Figure Of :
   {2,6,9} of size 648
   {4,6,9} of size 1296
   {6,6,9} of size 1944
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,3}*108
   9-fold quotients : {6,3}*36
   27-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,18}*648d
   3-fold covers : {6,9}*972a, {6,9}*972b, {6,9}*972c, {6,9}*972d, {18,9}*972j
   4-fold covers : {6,36}*1296c, {12,18}*1296g, {6,9}*1296c, {12,9}*1296d
   5-fold covers : {6,45}*1620c
   6-fold covers : {6,18}*1944a, {6,18}*1944d, {6,18}*1944f, {6,18}*1944h, {18,18}*1944ac, {6,18}*1944q
Permutation Representation (GAP) :

s0 := (2,3)(5,6)(8,9);;
s1 := (2,3)(4,8)(5,7)(6,9);;
s2 := (1,4)(2,6)(3,5)(8,9);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >;

References : None.
to this polytope