New for: D1, D3, D4, D5
fields. However, their combinatorial properties are not well known.
In this talk, we present some recent 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.