  The simple cubic lattice defines a set of points at regular distances. The
volume of the Voronoi cells around each point may serve as a weight for
integration over the entire space. We add interstitial points to this grid
according to the rule that these have maximum distance to the existing points,
or by the equivalent rule that they are placed at the vertices of the Voronoi
cells of the existing lattice. Choices of that kind appear in numerical
sampling with maximum independent data points if the numerical expense of
computing values represented at the lattice points is high. The volumes and
shapes of the Voronoi cells of these enriched/supersampled lattices are
discussed in detail while this insertion is recursively executed three times in
succession.
