How can the packing density of a set of congruent ellipsoids be calculated? I'm dealing with prolate spheroids so technically I do not need the general answer for ellipsoids, but my abstract mind loves more general answers. If calculating an exact value is too difficult, an estimate which is accurate enough to allow me to compare the relative packing densities of different sizes of spheroids is sufficient.
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The densest known packing of ellipsoids of any kind, including prolate spheroids, is given in this paper. From the abstract: