A total of 126 hypothetical zeolite structures have been modeled in the composition AlPO4. The framework topologies are those derived by tiling theory and comprise uninodal structures based on simple or quasi-simple tilings. Atomistic calculations have been used to optimize and evaluate each structure, and compare it to that of the SiO2 polymorph possessing the same topology. Characteristic properties including relative lattice energies, framework density, coordination sequences, accessible volumes, surface areas, average bond distances and angles, and the degree of distortion of the TO4 tetrahedra were calculated. The AlPOs are found to be more stable relative to berlinite than the zeolites are relative to quartz. The AlPO and SiO2 polymorphs show the same relationships between framework density and lattice energies, as well as between framework density and accessible volume, enabling us to predict whether individual hypothetical AlPO/silica polymorphs can be expected to be thermodynamically feasible. We describe eight hypothetical AlPO frameworks, which we believe to be interesting and thermodynamically feasible.