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Recent experiments on vesicles formed from block copolymers with liquid-crystalline side chains reveal a rich variety of vesicle morphologies.The additional internal order(“structure”)devel-oped by these selfassembled block copolymer vesicles can lead to significantly deformed vesicles as a result of the delicate inter-play between two-dimensional ordering and vesicle shape.The inevitable topological defects in structured vesicles of spherical topology also play an essential role in controlling the final vesicle morphology.Here we develop a minimal theoretical model for the morphology of the membrane structure with internal nematic/smectic order.Using both analytic and numerical approaches,we show that the possible low free energy morphologies include nano-size cylindrical micelles(nano-fibers),faceted tetrahedral vesicles,and ellipsoidal vesicles,as well as cylindrical vesicles.The tetrahedral vesicle is a particularly fascinating example of a faceted liquid-crystalline membrane.Faceted liquid vesicles may lead to the design of supramolecular structures with tetrahedral symmetry and new classes of nano-carriers.