Title: Minkowski sums of polytopes oriented in general directions

Minkowski sums is a basic operation with applications in many fields. However, their combinatorial properties are not well known. We present in this talk some results on sums of polytopes oriented in general directions. In particular, we prove the exact maximal number of faces for sums of any number of 3-dimensional polytopes. We also introduce a conjecture on vertices in higher dimensions. Finally, we present an algorithm computing the facets of Minkowski sums of polytopes oriented in general directions.