2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59672We show that, if the interior of a lattice d-polytope P contains at least one lattice point, then it contains a lattice point whose coefficient of asymmetry with respect to P is at most b for some number b depending on d only. As an application, we obtain new upper bounds on the volume of a lattice polytope given the number of lattice points in its interior.14 pages (paper) + 22 pages (C code) Submitted to MathematikaCombinatoricsMetric GeometryNumber Theory52B20text