A polymeric membrane material for efficient water desalination based on a cross-linked type I bicontinuous cubic (Q(I)) lyotropic liquid crystal (LLC) assembly is described. This ordered, nanoporous, polymer material is formed by the self-assembly of a cross-linkable gemini amphiphile in water and contains interpenetrating organic networks separated from one another by a continuous, ultrathin water layer surface (ca. 0.75 nm gap spacing) with overall cubic symmetry. Supported membranes of this material are produced by hot-pressing the initial LLC monomer gel at high pressure through a commercial microporous hydrophilic membrane support at 70 degrees C and then radically photocross-linking the infused Q(I) monomer phase. In stirred dead-end water filtration tests, the resulting 40-mu m thick, optically transparent, supported LLC membranes exhibit 95-99.9% rejection of dissolved salt ions, neutral molecules and macromolecules, and molecular ions in the 0.64-1.2 nm size range in a single pass. This rejection performance is slightly better than that of a commercial reverse osmosis (RO) membrane for the same solutes under the same test conditions, and significantly better than that of a commercial porous nanofiltration membrane. The LLC polymer material also exhibits a thickness- and pressure-normalized water permeability that is similar to or just slightly lower than the dense active layer materials used in current RO membranes. It is believed that the 3-D interconnected water manifold system in the cross-linked Q(I)-phase material allows small water molecules (0.27 nm kinetic diameter) to pass through with good efficiency, while effectively rejecting dissolved solutes close in size to, or larger than, the about 0.75 nm water layer gap spacing.