AN ANALOGUE OF THE ALEKSANDROV PROJECTION THEOREM FOR CONVEX LATTICE POLYGONS

Let K and L be origin-symmetric convex lattice polytopes in R-n. We study a discrete analogue of the Aleksandrov projection theorem. If for every u is an element of Z(n), the sets (K boolean AND Z(n))| u(perpendicular to) and (L boolean AND Z(n))|u(perpendicular to) have the same number of points, is K = L? We give a positive answer to this problem in Z(2) under the additional hypothesis that (2K boolean AND Z(2))| u(perpendicular to) and (2L boolean AND Z(2))| u(perpendicular to) have the same number of points for every u is an element of Z(n).