  The main result of this paper is an inequality relating the lattice point
enumerator of a 3-dimensional, 0-symmetric convex body and its successive
minima. This is an example of generalization of Minkowski's theorems on
successive minima, where the volume is replaced by the discrete analogue, the
lattice point enumerator. This problem is still open in higher dimensions,
however, we introduce a stronger conjecture that shows a possibility of proof
by induction on the dimension.
