Dense packings of the Platonic and Archimedean solids

  title={Dense packings of the Platonic and Archimedean solids},
  author={Salvatore Torquato and Yang Jiao},
Dense particle packings have served as useful models of the structures of liquid, glassy and crystalline states of matter, granular media, heterogeneous materials and biological systems. Probing the symmetries and other mathematical properties of the densest packings is a problem of interest in discrete geometry and number theory. Previous work has focused mainly on spherical particles—very little is known about dense polyhedral packings. Here we formulate the generation of dense packings of… Expand
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