Dense crystalline dimer packings of regular tetrahedra
Statistical Mechanics
2010-07-27 v3 Soft Condensed Matter
Metric Geometry
Abstract
We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], 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
Cite
@article{arxiv.1001.0586,
title = {Dense crystalline dimer packings of regular tetrahedra},
author = {Elizabeth R. Chen and Michael Engel and Sharon C. Glotzer},
journal= {arXiv preprint arXiv:1001.0586},
year = {2010}
}
Comments
43 pages, revision of the proofs and the appendices, data for small unit cell packings in appendix D