Dense Crystalline Dimer Packings of Regular Tetrahedra

We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856341 .... 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.