Dense Periodic Packings of Tetrahedra with Small Repeating Units

Yoav Kallus, Veit Elser, Simon Gravel

Abstract: We present a one-parameter family of periodic packings of regular tetrahedra, with the packing fraction 100/117≈0.8547, that are simple in the sense that they are transitive and their repeating units involve only four tetrahedra. The construction of the packings was inspired from results of a numerical search that yielded a similar packing. We present an analytic construction of the packings and a description of their properties. We also present a transitive packing with a repeating unit of two tetrahedra and a packing fraction \(\frac{139+40\sqrt{10}}{369}\approx0.7194\).