Dense crystalline dimer packings of regular tetrahedra

TL;DR

This paper introduces a new dense crystalline packing of regular tetrahedra with a density of approximately 0.8563, demonstrating its potential optimality within certain parameters and contributing to understanding tetrahedral packings.

Contribution

It presents the densest known crystalline packing of regular tetrahedra with a specific unit cell structure and establishes its maximal density within a three-parameter family.

Findings

Achieved a packing density of 0.856347.

Identified the packing as potentially optimal for small periodic cells.

Demonstrated the packing's maximal density within a specific family.

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.