The Symmetry and Order of Densest Packings of Space

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The PI has recently obtained new results on qualitative features of packings : proof of an abrupt change (phase transition) between low and high density packings of a certain deformed disk in the plane, and the experimental discovery of a phase transition in packings of sand (that is, with anisotropy produced by gravity) as density is varied.These results give a uniform approach to understanding certain qualitative features of the geometry of packings, linking research areas in unexpected and fruitful ways, and using a variety of mathematical techniques unusual in the traditional approaches to such studies.