  The objective of this paper is to present two types of results on Minkowski
sums of convex polytopes. The first is about a special class of polytopes we
call perfectly centered and the combinatorial properties of the Minkowski sum
with their own dual. In particular, we have a characterization of face lattice
of the sum in terms of the face lattice of a given perfectly centered polytope.
Exact face counting formulas are then obtained for perfectly centered simplices
and hypercubes. The second type of results concerns tight upper bounds for the
f-vectors of Minkowski sums of several polytopes.

Combinatorics