Chiral Polytope of Type {3,6,18}

This page is part of the Atlas of Small Chiral Polytopes
Regular Cover :{3,6,18}*1944a with group SmallGroup(1944,949) = (C33 ⋊ (D9 x C2)) x C2of order 1944
Rank : 4
Schlafli Type : {3,6,18}
Rotation Group : SmallGroup(324,77) = ((C33 ⋊ C3) ⋊ C2) x C2 of order 324
Number of vertices, edges, etc : 3, 9, 54, 18
If Aut({3,6,18}*1944a)=<s0, s1, s2, s3>, then this chiral polytope is ({3,6,18}*1944a)/N, where
N=<s1*s3*s2*s1*s3*s2*s1*s3*s2*s3*s2*s1*s3*s2*s3*s2> of order 3
Facet : Regular {3,6}*36
Vertex Figure : Chiral Quotient of {6,18}*648a Finitely Presented Group Representation of the Rotation Group(GAP) : 
F := FreeGroup("sig1","sig2","sig3");;
sig1 := F.1;;  sig2 := F.2;;  sig3 := F.3;;  
rels := [ sig1*sig1*sig1, sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2^-1*sig3^-1*sig2^-1*sig3^-1, 
sig1^-1*sig3*sig1*sig2*sig3*sig2^-1, sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1, 
sig2*sig3^-1*sig3^-1*sig2*sig3^-1*sig3^-1, sig1*sig3*sig1*sig3*sig1*sig3*sig3*sig3*sig3 ];;
rotpoly := F / rels;;
Finitely Presented Group Representation of the Rotation Group (Magma) : 
rotpoly<sig1,sig2,sig3> := Group< sig1,sig2,sig3 | sig1*sig1*sig1, sig1^-1*sig2^-1*sig1^-1*sig2^-1, 
sig2^-1*sig3^-1*sig2^-1*sig3^-1, sig1^-1*sig3*sig1*sig2*sig3*sig2^-1, sig1*sig2^-1*sig2^-1*sig2^-1*sig1*sig2^-1, 
sig2*sig3^-1*sig3^-1*sig2*sig3^-1*sig3^-1, sig1*sig3*sig1*sig3*sig1*sig3*sig3*sig3*sig3 >;