This article investigates the three-dimensional self-assembly of submillimeter scale polyhedra using surface forces. Using a combination of energy landscape calculations and experiments, we investigate the influence of patterns of hydrophobic surfaces on generating defect-free, closed-packed aggregates of polyhedra, with a focus on cubic units. Calculations show that surface patterning strongly affects the interaction between individual units as well as that of the unit with the growing assembly. As expected, an increase in the hydrophobic surface area on each face results in larger global minima. However, it is the distribution of hydrophobic surface area on each cubic face that is strongly correlated to the energetic parameters driving low-defect assembly. For patterns with the same overall area, minimizing the radius of gyration and maximizing the angular distribution leads to steep energy curves, with a lower propensity for entrapment in metastable states. Experimentally, 200-500 mu m sized metallic polyhedra were fabricated using a self-folding process, and the exposed surfaces were coated with a hydrophobic polymer. Cubes with surface patterns were agitated to cause aggregative self-assembly. Experimental results were consistent with energy calculations and suggest that geometric patterns with large overall areas, low radii of gyration, and high angular distributions result in efficient and low-defect assembly.