Discrete & Computational Geometry

, Volume 44, Issue 2, pp 245–252

Dense Periodic Packings of Tetrahedra with Small Repeating Units

Authors

    • Laboratory of Atomic and Solid-State PhysicsCornell University
  • Veit Elser
    • Laboratory of Atomic and Solid-State PhysicsCornell University
  • Simon Gravel
    • Department of GeneticsStanford University School of Medicine
Article

DOI: 10.1007/s00454-010-9254-3

Cite this article as:
Kallus, Y., Elser, V. & Gravel, S. Discrete Comput Geom (2010) 44: 245. doi:10.1007/s00454-010-9254-3

Abstract

We present a one-parameter family of periodic packings of regular tetrahedra, with the packing fraction 100/117≈0.8547, that are simple in the sense that they are transitive and their repeating units involve only four tetrahedra. The construction of the packings was inspired from results of a numerical search that yielded a similar packing. We present an analytic construction of the packings and a description of their properties. We also present a transitive packing with a repeating unit of two tetrahedra and a packing fraction \(\frac{139+40\sqrt{10}}{369}\approx0.7194\).

Keywords

PackingHilbert problemCrystallographyPolyhedraRegular solid

Copyright information

© Springer Science+Business Media, LLC 2010