Deep hole

in a lattice

Let $P$ be a collection of points in ${\mathbf R}^n$ (usually a lattice of points). A hole is a point of ${\mathbf R}^n$ whose distance to $P$ is a local maximum. A deep hole is a point of ${\mathbf R}^n$ whose distance to $P$ is the absolute maximum (if such exists).

If $P$ is a lattice, then the holes are precisely the vertices of the Voronoi cells (cf. Voronoi diagram; Parallelohedron).

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