The design of new and interesting inorganic frameworks is an ongoing challenge in materials sciences. New structures containing double-four-ring (D4R) units have recently received particular attention. The present work focuses on the computational design of new three-dimensional frameworks made of D4R units exclusively. In a first step, our simulations explore the possible ways to assemble predefined D4R units in 3D space using a sophisticated cascade of simulated annealing/minimizations steps (autoassembly of secondary building units method). While the existing zeotype topologies were successfully generated, new topologies were predicted including very open frameworks containing new types of cages, In a second step, lattice energy minimizations were performed to estimate the viability of these hypothetical frameworks as silicate, aluminophosphaste, and gallophosphate candidates. When comparing the hypothetical structures to existing compounds, our results raise the challenging question of the appropriate chemical composition that should be aimed at for a given framework topology of interest.