Bezdek and Kuperberg have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2) - 6sqrt(3) - 2π) π)/72 = 0.753355... (OEIS A093824), greater than the maximum density of π/(3sqrt(2))≈0.74048 (OEIS A093825) that is possible for sphere packing, as established by proof of the Kepler conjecture. Furthermore, J. Wills has modified the ellipsoid packing to yield an even higher density of 0.7585....

ellipsoid | Kepler conjecture | random close packing | sphere packing