A model for the dual of the generalised hexagon H(q), q odd

Bader and Lunardon found a model for the dual of the split Cayley hexagon H(q), q odd and not a power of 3, using a twisted cubic in PG(3,q). We propose a slightly modified version of this model which also works if q is a power of 3, and discuss the connection with a model for the dual of the twisted triality hexagon H(q3,q) described by Lunardon.