Keller’s cube-tiling conjecture is false in high dimensions
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- by Jeffrey C. Lagarias and Peter W. Shor PDF
- Bull. Amer. Math. Soc. 27 (1992), 279-283 Request permission
Abstract:
O. H. Keller conjectured in 1930 that in any tiling of ${\mathbb {R}^n}$ by unit n-cubes there exist two of them having a complete facet in common. O. Perron proved this conjecture for $n \leq 6$. We show that for all $n \geq 10$ there exists a tiling of ${\mathbb {R}^n}$ by unit n-cubes such that no two n-cubes have a complete facet in common.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 27 (1992), 279-283
- MSC (2000): Primary 52C22; Secondary 05B45
- DOI: https://doi.org/10.1090/S0273-0979-1992-00318-X
- MathSciNet review: 1155280