Bárány, I., Howe, R. & Lovász, L. Combinatorica (1992) 12: 135. doi:10.1007/BF01204716
Given a polyhedronP⊂ℝ we writePI for the convex hull of the integral points inP. It is known thatPI can have at most135-2 vertices ifP is a rational polyhedron with size φ. Here we give an example showing thatPI can have as many as Ω(ϕn−1) vertices. The construction uses the Dirichlet unit theorem.