Remarks on the density of sphere packings in three dimensions (Q684405)

The author studies the density of sphere packings of spheres of equal radius by using the Delaunay decomposition. A local notion of density for sphere packings in \(\mathbb{R}^ 3\) is defined; this density has a bound which is conjectured to be \(0.740873\dots\), but because of a small perturbation it is \(\pi/\sqrt{18}\). The local measure of density coincides with the actual density for the face-centered cubic and hexagonal-close-packings.