Translational tiling of the plane with a set of seven orthogonally convex polyominoes is undecidable.
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 of the Plane with Orthogonally Convex Polyominoes
Translational tiling of the plane with a set of seven orthogonally convex polyominoes is undecidable.