Dense crystalline dimer packings of regular tetrahedra

Details Dense crystalline dimer packings of regular tetrahedra Dense crystalline dimer packings of regular tetrahedra

2010-01-05

arxiv.org/abs/1001.0586v3

Discrete & Computational Geometry 44, 253 (2010)

Physics

Condensed Matter

Statistical Mechanics

43 pages, revision of the proofs and the appendices, data for small unit cell packings in appendix D

Scientific paper

10.1007/s00454-010-9273-0

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.

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