The Q I phase exists in a number of space groups as shown in Fig 1 . Experimental data for these gemini-shape LLC monomers are consistent with all three of the most commonly identified space groups, the primitive (Im3m), Schwarz diamond (Pn3m), and gyroid (Ia3d ). Specifically, the experimental self-assembled systems show Q I phases, indicated by a black optical texture under PLM and PXRD patterns with d spacings in the ratio of 1/ (6) : 1/ (8), but the higher-order PXRD reflections needed to distinguish between space groups are not present. The Q I phases are examples of triply periodic minimal surfaces, which are mathematically well-studied. As a result, each of these space groups has a nodal approximation of the form F (x, y, z) = 0 as shown in Equations 1-3.