  O. H. Keller conjectured in 1930 that in any tiling of $\Bbb R^n$ by unit
$n$-cubes there exist two of them having a complete facet in common. O. Perron
proved this conjecture for $n\le 6$. 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.
