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For questions about mathematical tiling.

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Detecting tilings by toric geometry

If you look at the Delaunay tiling which is dual to the Voronoi tiling $P+\mathbb Z^n$, then the polytopes in that tiling and the corresponding toric varieties have a clear geometric meaning: they describe … Then the $(n-1)$-skeleton of the Voronoi tiling modulo $\mathbb Z^n$ is the theta divisor on $A$. See Mikhalkin-Zharkov http://arxiv.org/abs/math/0612267 for more details. …
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