Discrete & Computational Geometry

, Volume 44, Issue 2, pp 253–280

Dense Crystalline Dimer Packings of Regular Tetrahedra

  • Elizabeth R. Chen
  • Michael Engel
  • Sharon C. Glotzer

DOI: 10.1007/s00454-010-9273-0

Cite this article as:
Chen, E.R., Engel, M. & Glotzer, S.C. Discrete Comput Geom (2010) 44: 253. doi:10.1007/s00454-010-9273-0


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.


Crystallography Packing Regular solid Hilbert problem 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Elizabeth R. Chen
    • 1
  • Michael Engel
    • 2
  • Sharon C. Glotzer
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of Chemical EngineeringUniversity of MichiganAnn ArborUSA
  3. 3.Department of Materials Science and EngineeringUniversity of MichiganAnn ArborUSA

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