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The impact of topological defects associated with grain boundaries (GB defects) on the electrical, optical, magnetic, mechanical and chemical properties of nanocrystalline materials^, is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations^{, –}. Here we demonstrate that precise control of the heteroepitaxy of colloidal polyhedral nanocrystals enables ordered grain growth and can thereby produce material samples with uniform GB defects. We illustrate our approach with a multigrain nanocrystal comprising a Co₃O₄ nanocube core that carries a Mn₃O₄ shell on each facet. The individual shells are symmetry-related interconnected grains, and the large geometric misfit between adjacent tetragonal Mn₃O₄ grains results in tilt boundaries at the sharp edges of the Co₃O₄ nanocube core that join via …