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# A criterion for finite lattice coverings

## Abstract

For a centrally symmetric convex $$K \subset E^2$$ and a covering lattice L for K, a lattice polygon P is called a covering polygon, if $$P \subset (L \cap P) + K$$. We prove that P is a covering polygon, if and only if its boundary bd(P) is covered by (L ∩ P) + K. Further we show that this characterization is false for non-symmetric planar convex bodies and in Euclidean d–space, d ≥ 3, even for the unit ball K = B d.

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