Exact constructions of a family of dense periodic packings of tetrahedra

S. Torquato and Y. Jiao
Phys. Rev. E 81, 041310 – Published 30 April 2010

Abstract

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered “dimer” packings of tetrahedra, including the densest known packings with density ϕ=40004671=0.856347. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

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  • Received 31 January 2010

DOI:https://doi.org/10.1103/PhysRevE.81.041310

©2010 American Physical Society

Authors & Affiliations

S. Torquato1,2,3,4,5,6 and Y. Jiao6

  • 1Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 3Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 4Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
  • 5School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
  • 6Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 81, Iss. 4 — April 2010

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