  It is well known that all cells of the Voronoi diagram of a Delaunay set are
polytopes. For a finite point set, all these cells are still polyhedra. So the
question arises, if this observation holds for all discrete point sets: Are
always all Voronoi cells of an arbitrary, infinite discrete point set
polyhedral? In this paper, an answer to this question will be given. It will be
shown that all Voronoi cells of a discrete point set are polytopes if and only
if every point of the point set is an inner point. Furthermore, the term of a
locally finitely generated discrete point set will be introduced and it will be
shown that exactly these sets have the property of possessing only polyhedral
Voronoi cells.
