View article

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \({\varphi}={\pi}{/}\sqrt{18}{\approx}0.74\) \end{document}. It is also well known that certain random (amorphous) jammed packings have φ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely—up to φ= 0.68 to 0.71for spheroids with an aspect ratio close to that of M&M's Candies—and even approach φ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the …