In geometry, ellipsoid packing is the problem of arranging identical ellipsoid throughout three-dimensional space to fill the maximum possible fraction of space. The currently densest known packing structure for ellipsoid has two candidates,a simple monoclinic crystal with two ellipsoids of different orientations anda square-triangle crystal containing 24 ellipsoids in the fundamental cell. 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 and . Any ellipsoids with aspect ratios larger than one can pack denser than spheres.
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