# Keller’s cube-tiling conjecture is false in high dimensions

@article{Lagarias1992KellersCC,
title={Keller’s cube-tiling conjecture is false in high dimensions},
author={J. Lagarias and P. Shor},
journal={Bulletin of the American Mathematical Society},
year={1992},
volume={27},
pages={279-283}
}
• Published 1992
• Mathematics
• Bulletin of the American Mathematical Society
O. H. Keller conjectured in 1930 that in any tiling of R n by unit n-cubes there exist two of them having a complete facet in common. 0. Perron proved this conjecture for n ≤ 6. We show that for all n ≥ 10 there exists a tiling of R n by unit n-cubes such that no two n-cubes have a complete facet in common
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