The structures of self-assembled monolayers formed by chemisorption of octadecanethiol onto the surfaces of GaAs(001), (110), (111-A)-Ga, and (111-B)-As have been characterized in detail by a combination of X-ray photoelectron, near-edge X-ray absorption fine structure, and infrared spectroscopies and grazing incidence X-ray diffraction. In all cases, the molecular lattices are ordered with hexagonal symmetry, even for the square and rectangular intrinsic substrate (001) and (110) lattices, and the adsorbate lattice spacings are all incommensurate with their respective intrinsic substrate lattices. These results definitively show that the monolayer organization is driven by intermolecular packing forces to assemble in a hexagonal motif, such as would occur in the approach to a limit for an energetically featureless surface. The accompanying introduction of strain into the soft substrate surface lattice via strong S substrate bonds forces the soft substrate lattice to compliantly respond, introducing quasi-2D strain. A notably poorer organization for the (111-A)-Ga case compared to the (111-B)-As and other faces indicates that that the Ga-terminated surface lattice is more resistant to adsorbate packing-induced stress. Overall, the results show that surface molecular self-assembly must be considered as a strongly cooperative process between the substrate surface and the adsorbate and that inorganic substrate surfaces should not be considered as necessarily rigid when strong intermolecular adsorbate packing forces are operative.