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Published online by Cambridge University Press: 26 February 2010
Let K be a convex body (compact convex set with interior points) in d-dimensional euclidean space Ed, let D(K) denote its diameter, Δ(K) its minimal width, and
the number of lattice points (points of Ed with integer coordinates) in the interior of K. If G0(K) = 0, we call K lattice-point-free; in what follows, K will always be a lattice-point-free convex body.