Mixtures of cationic and anionic surfactants crystallized at various ratios in the absence of added salt form micrometer-sized colloids. Here, we propose and test a general mechanism explaining how this ratio controls the shape of the resulting colloidal structure, which can vary from nanodiscs to punctured planes; during cocrystallization, excess (nonstoichiometric) surfactant accumulates on edges or pores rather than being incorporated into crystalline bilayers. Molecular segregation then produces a sequence of shapes controlled by the initial mole ratio only. Using freeze-fracture electron microscopy, we identified three of these states and their corresponding coexistence regimes. Fluorescence confocal microscopy directly showed the segregation of anionic and cationic components within the aggregate. The observed shapes are consistently reproduced upon thermal cycling, demonstrating that the icosahedral shape corresponds to the existence of a local minimum of bending energy for facetted icosahedra when the optimal amount of excess segregated material is present.