A finite tile in ℤ³ admits a translational tiling but no fully periodic tiling; its unit-cube thickening has the same property in ℝ³ even with arbitrary real translations.
A finite tile in ℤ³ admits a translational tiling but no fully periodic tiling; its unit-cube thickening has the same property in ℝ³ even with arbitrary real translations.
A finite tile in ℤ³ admits a translational tiling but no fully periodic tiling; its unit-cube thickening has the same property in ℝ³ even with arbitrary real translations.
If correct, lowers a known periodic-tiling counterexample to the least possible lattice dimension, three.
Can a finite translational tile in dimension three tile without any fully periodic tiling?
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OpenAI reports a nonperiodic translational tile in dimension three
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