A geometric approach for the upper bound theorem for Minkowski sums of convex polytopes

Menelaos I. Karavelas, Eleni Tzanaki

We derive tight expressions for the maximum number of $k$-faces, $0\le k\le d-1$, of the Minkowski sum, $P_1+...+P_r$, of $r$ convex $d$-polytopes $P_1,...,P_r$ in ${\mathbb{R}}^d$…