  Consider a finite connected graph possibly with multiple edges and loops. In
discrete geometric analysis, Kotani and Sunada constructed the crystal
associated to the graph as a standard realization of the maximal abelian
covering of the graph. As an application of what the author showed in an
earlier paper with Seshadri as a by-product of Geometric Invariant Theory, he
shows that the Voronoi tiling (also known as the Wigner-Seitz tiling) is hidden
in the crystal, that is, the crystal does not intrude the interiors of the
top-dimensional Voronoi cells. The result turns out to be closely related to
the tropical Abel-Jacobi map of the associated compact tropical curve.
