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

@article{Lagarias1992KellersCC,
  title={Keller’s cube-tiling conjecture is false in high dimensions},
  author={Jeffrey C. Lagarias and Peter W. Shor},
  journal={Bulletin of the American Mathematical Society},
  year={1992},
  volume={27},
  pages={279-283}
}
  • J. LagariasP. Shor
  • Published 1 March 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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