  For a convex polytope P with rational vertices, we count the number of
integer points in integral dilates of P and its interior. The Ehrhart-Macdonald
reciprocity law gives an intimate relation between these two counting
functions. A similar counting function and reciprocity law exists for the sum
of all solid angles at integer points in dilates of P. We derive a unifying
generalization of these reciprocity theorems which follows in a natural way
from Brion's Theorem on conic decompositions of polytopes.
