Английская Википедия:Ellipsoid packing

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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[1] and a square-triangle crystal containing 24 ellipsoids[2] in the fundamental cell. The former monoclinic structure can reach a maximum packing fraction around <math>0.77073</math> for ellipsoids with maximal aspect ratios larger than <math>\sqrt{3}</math>. 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 <math>\alpha:\sqrt{\alpha}:1</math> and <math>\alpha \in (1.365,1.5625)</math>. Any ellipsoids with aspect ratios larger than one can pack denser than spheres.

See also

References

Шаблон:Reflist

Шаблон:Packing problems