2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124642In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of n unit hypercubes in the d-dimensional Euclidean space. For d=2 we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each n.13 pages, 10 figuresCombinatorics05B50; 05D99; 52C99text