Deciding translational tiling of Z^4 by three connected polyhypercubes is undecidable, shown by reduction from Wang's domino problem.
Berger, The undecidability of the domino problem, Memoirs of the American Mathematical Society , 66(1966), 1-72
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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.