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Self-assembling dendrimers have facilitated the discovery of periodic and quasiperiodic arrays of supramolecular architectures and the diverse functions derived from them. Examples are liquid quasicrystals and their approximants plus helical columns and spheres, including some that disregard chirality. The same periodic and quasiperiodic arrays were subsequently found in block copolymers, surfactants, lipids, glycolipids, and other complex molecules. Here we report the discovery of lamellar and hexagonal periodic arrays on the surface of vesicles generated from sequence-defined bicomponent monodisperse oligomers containing lipid and glycolipid mimics. These vesicles, known as glycodendrimersomes, act as cell-membrane mimics with hierarchical morphologies resembling bicomponent rafts. These nanosegregated morphologies diminish sugar–sugar interactions enabling stronger binding to sugar-binding proteins than densely packed arrangements of sugars. Importantly, this provides a mechanism to encode the reactivity of sugars via their interaction with sugar-binding proteins. The observed sugar phase-separated hierarchical arrays with lamellar and hexagonal morphologies that encode biological recognition are among the most complex architectures yet discovered in soft matter. The enhanced reactivity of the sugar displays likely has applications in material science and nanomedicine, with potential to evolve into related technologies.