Unimodular covers of 3-dimensional parallelepipeds and Cayley sums

We introduce unimodular triangulations, covers and the integer decomposition property of lattice polytopes, and briefly touch on motivations for their study. We then show that the following special classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds and the class of Cayley sums of two polytopes where one is a weak Minkowski summand of the other. Based on joint work with Francisco Santos.