Maximizing the placement of congruent polyhedrain a parallelepiped container

Given multiple identical polyhedral objects and a parallelepiped container, how should one place the objects so that the largest number fits inside the container? This simple question is important in many applications, yet the answer is elusive. In fact, we know of no published solution for this very general formulation. Still, in many circumstances, further restrictions apply, resulting in a large number of variations requiring different algorithmic strategies. In this presentation we will further formalize the problem, present some of its many variations, and in particular one that applies to the stereolithographic rapid prototyping technology.