Q phases are significantly harder to model than the hexagonal phase, as they generally only form in a narrow range of composition and temperature space. Besides the narrow phase space, the three-dimensional periodicity of the Q I phase also adds to the complexity. In hexagonal and lamellar phases, which are periodic in two and one dimension respectively, the crystal periodicity can be maintained in the diagonal direction even when the periodicity of the simulation cell does not match the periodicity of the crystal. Such adjustment is not possible for cubic crystals. As a result, even a small discrepancy between the periodicity of the crystal and periodic boundary condition in simulation can inhibit the formation of the correct phase due to unnatural interactions with periodic images. Whether Q phases are formed by self-assembly of monomers or by placing the monomer in the right assembly in a bottomup fashion, they tend to eventually morph into other phases that have fewer constraints from periodicity. In literature, there are only a handful of successful atomistic models of Q phases of selfassembled monomers, and stability of the cubic phase is a known issue. The majority of models used in modeling bicontinuous systems are coarse-grained (CG), whereas, for a detailed understanding of selective molecular transport, atomistic detail is necessary. To that end, we develop in this paper procedures for building atomistic models of the Q structure that are, at minimum, metastable over substantial (1 µs) simulation lengths. We use a combination of mathematical constraints, CG simulation, and atomistic modeling to rapidly explore the right conditions for the formation of the Q structure as well as the route to modify them for desired structural and transport properties. Moreover, we characterize the pores produced in such a system and the transport within these pores. These procedures will hopefully accelerate and guide the design of new monomers used for self-assembled porous materials as well as help understand their function.