Amphiphilic molecules can form closed-shell structures that are determined by competing attractive and repulsive forces. Since supramolecular shape has its roots in intermolecular interactions, the interplay of electrostatic, hydrophobic, and steric forces can generate nonspherical structures. Here we show that anionic and cationic amphiphiles of unequal charge can coassemble into small buckled vesicles and present a physical argument that explains this phenomenon. The strong electrostatic interaction between the +3 and -1 head groups increases the cohesion energy of the amphiphiles and favors the formation of two-dimensional, flat ionic domains on the vesicle surface, resulting in edges and a buckled shape.