Chiral Polytope of Type {18,6,3}

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