We report a general method of constructing microporous, cubic frameworks from eight different high symmetry small clusters of ZnO, which were previously predicted via the application of an evolutionary algorithm. Using interatomic potentials, the lattice energies of the structures formed are computed. We analyse the relative stabilities within particular subsets of these periodic structures, and show that frameworks constructed from edge-sharing units of clusters with the T(h) point group are predicted to be much more stable than those with T(d). Our results have general implications for the nanostructures of systems whose bulk structures are based on tetrahedral coordination.