Minkowski sum of polytopes

Summary

The Minkowski sum of two convex polytopes $P$ and $Q$ is the set of all sums $p + q$ with $p \in P$ and $q \in Q$. It is again a convex polytope, and it is the special case of Minkowski addition for polytopes. Its faces are sums of faces of $P$ and $Q$. Its normal fan is the common refinement of the normal fans of $P$ and $Q$. Minkowski sums lead to zonotopes, to mixed volumes and to the Newton polytopes of products of polynomials.