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We propose a simple direct-sum method for the efficient evaluation of lattice sums in periodic solids. It consists of two main principles (i) the creation of a supercell that has the topology of a Clifford torus, which is a flat, finite, and borderless manifold; (ii) the renormalization of the distance between two points on the Clifford torus by defining it as the Euclidean distance in the embedding space of the Clifford torus. Our approach does not require any integral transformations nor any renormalization of the charges. We illustrate
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