On the exact maximum complexity of Minkowski sums of polytopes

Abstract

We present a tight bound On the exact maximum complexity of Minkowski sums of polytopes in ℝ3. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2,...,mk facets, respectively, is bounded from above by. Given k positive integers m1,m2,...,mk, we describe how to construct k polytopes with corresponding number of facets, such that the number of facets of their Minkowski sum is exactly. When k=2, for example, the expression above reduces to 4m1m2-9m1-9m2+26. © Springer Science+Business Media, LLC 2009.