Chiral Polytope of Type {9,6}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{9,6}*324a with group SmallGroup(324,37) = (C3 x C9) ⋊ D6of order 324
Rank : 3
Schlafli Type : {9,6}
Rotation Group : SmallGroup(54,6) = C9 ⋊ C6 of order 54
Number of vertices, edges, etc : 9, 27, 6
If Aut({9,6}*324a)=<s0, s1, s2>, then this chiral polytope is ({9,6}*324a)/N, where
N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3
Facet : (Regular) 9-gon
Vertex Figure : (Regular) 6-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;  
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig2^-1*sig1*sig1*sig2^-1, sig2*sig2*sig2*sig2*sig2*sig2, 
sig1*sig2*sig2*sig2*sig1^-1*sig1^-1*sig2^-1 ];;
rotpoly := F / rels;;
 
Finitely Presented Group Representation of the Rotation Group (Magma) :

rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig2^-1*sig1*sig1*sig2^-1, 
sig2*sig2*sig2*sig2*sig2*sig2, sig1*sig2*sig2*sig2*sig1^-1*sig1^-1*sig2^-1 >;