Dense Crystalline Dimer Packings of Regular Tetrahedra

@article{Chen2010DenseCD,
  title={Dense Crystalline Dimer Packings of Regular Tetrahedra},
  author={Elizabeth R. Chen and Michael Engel and Sharon C. Glotzer},
  journal={Discrete \& Computational Geometry},
  year={2010},
  volume={44},
  pages={253-280}
}
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… 
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