  In a previous paper (El. J. Combin. 6 (1999), R37), the author generalized
Ehrhart's idea of counting lattice points in dilated rational polytopes: Given
a rational polytope, that is, a polytope with rational vertices, we use its
description as the intersection of halfspaces, which determine the facets of
the polytope. Instead of just a single dilation factor, we allow different
dilation factors for each of these facets. We proved that, if our polytope is a
simplex, the lattice point counts in the interior and closure of such a
vector-dilated simplex are quasipolynomials satisfying an Ehrhart-type
reciprocity law. This generalizes the classical reciprocity law for rational
polytopes. In the present paper we complete the picture by extending this
result to general rational polytopes. As a corollary, we also generalize a
reciprocity theorem of Stanley.
