Decomposability of polytopes and polyhedra

In this paper decomposability of polytopes (and polyhedral sets) is studied by investigating the space of affine dependences of the vertices of the dual polytope. This turns out to be a fruitful approach and leads to several new results, as well as to simpler proofs and generalizations of known results. One of the new results is that a 3-polytope with more vertices than facets is decomposable; this leads to a characterization of the decomposability of 3-polytopes.