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Tiling 3D by Translates of a Single Polycube is Undecidable
We prove co-RE-completeness, and thus undecidability, of the following problem: given a single (connected) polycube, decide whether it tiles 3D Euclidean space by translations. We reduce from Wang tiling using the decorated two-prime Sudoku construction of Greenfeld and Tao and a cyclic encoding ada
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