Ellipsoid packing

In geometry, ellipsoid packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction of space.

The former monoclinic structure can reach a maximum packing fraction around

for ellipsoids with maximal aspect ratios larger than

The packing fraction of the square-triangle crystal exceeds that of the monoclinic crystal for specific biaxial ellipsoids, like ellipsoids with ratios of the axes

Any ellipsoids with aspect ratios larger than one can pack denser than spheres.