On Integer Points in Polyhedra: A Lower Bound

Given a polyhedron we write P(I) for the convex hull of the integral points in P. It is know that P(I) can have at most O(fi(n-1)) vertices if P is a rational polyhedron with size fi. Here we give an example showing that P(I) can have as many as Omega (fi(n-1)) vertices. The construction uses the Dirichlet unit theorem.Polyhedra, integral points, Dirichlet unit theorem