A computational method based on Monte Carlo cooling has been developed to quantitatively predict the geometric packing of rigid molecular units into screw, glide, and inversion aggregates using a force field containing only nonbonded and electrostatic terms. Of 60 aggregate structures selected at random from the Cambridge Structural Database (containing elements restricted to C, H, O, N, F, Cl, Br, I, S; no hydrogen bonds and only one molecule in the crystallographic asymmetric unit), 53 were found to lie at a local energy minimum which was 0.1-5.7 kcal above the global minimum but visually very different from it. The difference results from the existence of surface cavities in the global minimum structure created by the screw, glide, or inversion offset which are generally not fillable by parts of any other identical molecule. The electrostatic contribution to the total energy was found to be small, averaging 5% of the total energy and not structure determining. These results, taken together with our previous simulations for translation aggregates, confirm a generalized Aufbau principle implied by Kitaigrodskii, that the complex ordering of molecules in three dimensions can be broken down into substructures, each of which is in a local energy minimum. Implications of these results for the design of ordered molecular materials and for the quantitative predictions of monolayer packing and full 3-dimensional crystal packing are discussed.