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Dense Crystalline Dimer Packings of Regular Tetrahedra
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  • Published: 17 July 2010

Dense Crystalline Dimer Packings of Regular Tetrahedra

  • Elizabeth R. Chen1,
  • Michael Engel2 &
  • Sharon C. Glotzer2,3 

Discrete & Computational Geometry volume 44, pages 253–280 (2010)Cite this article

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Abstract

We present the densest known packing of regular tetrahedra with density \(\phi =\frac{4000}{4671}=0.856347\ldots\,\). Like the recently discovered packings of Kallus et al. and Torquato–Jiao, our packing is crystalline with a unit cell of four tetrahedra forming two triangular dipyramids (dimer clusters). We show that our packing has maximal density within a three-parameter family of dimer packings. Numerical compressions starting from random configurations suggest that the packing may be optimal at least for small cells with up to 16 tetrahedra and periodic boundaries.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Elizabeth R. Chen

  2. Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Michael Engel & Sharon C. Glotzer

  3. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Sharon C. Glotzer

Authors
  1. Elizabeth R. Chen
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  2. Michael Engel
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  3. Sharon C. Glotzer
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Corresponding author

Correspondence to Michael Engel.

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Cite this article

Chen, E.R., Engel, M. & Glotzer, S.C. Dense Crystalline Dimer Packings of Regular Tetrahedra. Discrete Comput Geom 44, 253–280 (2010). https://doi.org/10.1007/s00454-010-9273-0

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  • Received: 27 December 2009

  • Revised: 20 April 2010

  • Accepted: 16 May 2010

  • Published: 17 July 2010

  • Issue Date: September 2010

  • DOI: https://doi.org/10.1007/s00454-010-9273-0

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Keywords

  • Crystallography
  • Packing
  • Regular solid
  • Hilbert problem
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