  We investigate the maximum number of intersections between two polygons with
p and q vertices, respectively, in the plane. The cases where p or q is even or
the polygons do not have to be simple are quite easy and already known, but
when p and q are both odd and both polygons are simple, the problem is more
difficult. The conjectured maximum is (p-1)(q-1)+2 for all odd p and q.
