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Dense Periodic Packings of Tetrahedra with Small Repeating Units
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  • Published: 03 March 2010

Dense Periodic Packings of Tetrahedra with Small Repeating Units

  • Yoav Kallus1,
  • Veit Elser1 &
  • Simon Gravel2 

Discrete & Computational Geometry volume 44, pages 245–252 (2010)Cite this article

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  • 42 Citations

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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 \(\frac{139+40\sqrt{10}}{369}\approx0.7194\).

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Authors and Affiliations

  1. Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY, 14853, USA

    Yoav Kallus & Veit Elser

  2. Department of Genetics, Stanford University School of Medicine, Stanford, CA, 94305-5120, USA

    Simon Gravel

Authors
  1. Yoav Kallus
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  2. Veit Elser
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  3. Simon Gravel
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Corresponding author

Correspondence to Yoav Kallus.

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Cite this article

Kallus, Y., Elser, V. & Gravel, S. Dense Periodic Packings of Tetrahedra with Small Repeating Units. Discrete Comput Geom 44, 245–252 (2010). https://doi.org/10.1007/s00454-010-9254-3

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  • Received: 16 November 2009

  • Revised: 15 February 2010

  • Accepted: 15 February 2010

  • Published: 03 March 2010

  • Issue Date: September 2010

  • DOI: https://doi.org/10.1007/s00454-010-9254-3

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Keywords

  • Packing
  • Hilbert problem
  • Crystallography
  • Polyhedra
  • Regular solid
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