Abstract
In 1930, Keller conjectured that every tiling of RnRn by unit cubes contains a pair of cubes sharing a complete (n−1)(n−1)-dimensional face. Only 50 years later, Lagarias and Shor found a counterexample for all n≥10n≥10. In this note we show that neither a modification of Keller's conjecture to tiles of more complex shape is true.
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