The phase behavior of copper(II) bis(2-ethylhexyl) sulfosuccinate, Cu(AOT)(2)-isooctane-water, is determined over a wide domain. The system exhibits an extraordinarily diverse range of phases. The microstructures have been characterized by small-angle X-ray scattering, conductivity, and freeze fracture electron microscopy. It is shown that elementary considerations that require only notions of local curvature and global packing constraints are sufficient to determine microstructure.