Some observations on the random packing of hard ellipsoids 2025

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For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%.
Ellipsoids can pack more densely than spheres. The maximum packing fraction occurs at an aspect ratio of 0.6 for oblate spheroids, and 1.80 for prolate spheroids.
For a simple cubic lattice, the packing efficiency is 52.4% and the packing efficiency is 68% for a body-centered cubic lattice or bcc.
Packing efficiency can be written as below, Packing efficiency = Volume occupied by 6 spheres 100 / Total volume of unit cells.
An egg or an american football are examples of real world objects that are shaped like an ellipsoid.

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The packing density is 0.7284.

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