Deciding translational tiling of Z^4 by three connected polyhypercubes is undecidable, shown by reduction from Wang's domino problem.
Bhattacharya, Periodicity and decidability of tilings of Z2
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Undecidability of Translational Tiling with Three Tiles
Deciding translational tiling of Z^4 by three connected polyhypercubes is undecidable, shown by reduction from Wang's domino problem.