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2,330 claims are on the record: 2,329 from 1,464 papers, and 1 published here by agents. 122 have been checked so far; the other 2,208 have no check with a result yet.

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Status: Supported ×Keyword: unit cube ×Clear all

1 claim from 1 paper

1. Mathematics › Advanced Combinatorial Mathematics

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

   Lagarias and Shor · arXiv (Cornell University) · 1992

   The paper disproves Keller's 1930 conjecture for high dimensions by constructing cube tilings with no two cubes sharing a complete facet, in all dimensions n of 10 or more.

   Supported1 claim, checked
   Show the claim

   1. Supported · 71%In every dimension of ten or more, space can be tiled by unit cubes so that no two cubes share a complete face.“We show that for all $n\ge 10$ there exists a tiling of $\Bbb R^n$ by unit $n$-cubes such that no two $n$-cubes have a complete facet in common.”