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Tiling Theorem

Due to Lebesgue and Brouwer. If an $n$-D figure is covered in any way by sufficiently small subregions, then there will exist points which belong to at least $n+1$ of these subareas. Moreover, it is always possible to find a covering by arbitrarily small regions for which no point will belong to more than $n+1$ regions.

See also Tessellation, Tiling

© 1996-9 Eric W. Weisstein