About: Minkowski problem for polytopes

In the geometry of convex polytopes, the Minkowski problem for polytopes concerns the specification of the shape of a polytope by the directions and measures of its facets. The theorem that every polytope is uniquely determined up to translation by this information was proven by Hermann Minkowski; it has been called "Minkowski's theorem", although the same name has also been given to several unrelated results of Minkowski. The Minkowski problem for polytopes should also be distinguished from the Minkowski problem, on specifying convex shapes by their curvature.