Least Action Principle Of Crystal Formation Of Dense Packing Type And Kepler's Conjecture

The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal “known density” of B/√18. In 1611, Johannes Kepler had already “conjectured” that B/√18 should be the optimal “density” of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that B/√18 is the optimal density, and the establishing of the least action principle