Article

Discrete & Computational Geometry

, Volume 44, Issue 2, pp 253-280

First online:

Dense Crystalline Dimer Packings of Regular Tetrahedra

  • Elizabeth R. ChenAffiliated withDepartment of Mathematics, University of Michigan
  • , Michael EngelAffiliated withDepartment of Chemical Engineering, University of Michigan Email author 
  • , Sharon C. GlotzerAffiliated withDepartment of Chemical Engineering, University of MichiganDepartment of Materials Science and Engineering, University of Michigan

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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.

Keywords

Crystallography Packing Regular solid Hilbert problem