Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids
of densities arbitrarily close to
(OEIS A093824), greater than the maximum density of
(OEIS A093825) that is possible for sphere
packing (Sloane 1998), as established by proof of the Kepler
conjecture. Furthermore, J. Wills has modified the ellipsoid packing to
yield an even higher density of (Bezdek and Kuperberg 1991).
Donev et al. (2004) showed that a maximally random jammed state of M&Ms chocolate candies has a packing density of about 68%, or 4% greater than spheres.
Furthermore, Donev et al. (2004) also showed by computer simulations other
ellipsoid packings resulted in random packing densities approaching that of the densest
sphere packings, i.e., filling nearly 74% of space.
Bezdek, A. and Kuperberg, W. In Applied Geometry and Discrete Mathematics: The Victor Klee Festschrift (Ed. P. Gritzmann
and B. Sturmfels). Providence, RI: Amer. Math. Soc., pp. 71-80, 1991.Donev,
A.; Cisse, I.; Sachs, D.; Variano, E. A.; Stillinger, F. H.; Connelly,
R.; Torquato, S.; and Chaikin, P. M. "Improving the Density of Jammed Disordered
Packings using Ellipsoids." Science, 303, 990-993, 2004.Sloane,
N. J. A. "Kepler's Conjecture Confirmed." Nature395,
435-436, 1998.Sloane, N. J. A. Sequences A093824
and A093825 in "The On-Line Encyclopedia
of Integer Sequences."
(OEIS A093825) that is possible for sphere
packing (Sloane 1998), as established by proof of the Kepler
conjecture. Furthermore, J. Wills has modified the ellipsoid packing to
yield an even higher density of 
(Bezdek and Kuperberg 1991).
