Atom-atom potential calculations of planar lattices using a Buckingham potential for model alkane amphiphiles are reported. Of the seventeen planar space groups possible. it is shown that proper control of the amphiphiles' cross section, chirality and rigidity permits formation of centrosymmetric and/or non-centrosymmetric hexagonal, rectangular and oblique nets. The results suggest that all possible two-dimensional crystal nets may be formed thereby yielding new materials and model systems.