Given a combinatorial type of a convex polytope, what techniques are available for showing that it **cannot** be realized as a Voronoi cell of some point system?



How to show that convex polytope is not a Voronoi cell?
Every (non-flat) convex polytope is the Voronoi cell of a point in a set of points. Constructive proof: pick a point inside the polytope, and build its symmetric reflection along every facet of the polytope.


