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 \(\frac{139+40\sqrt{10}}{369}\approx0.7194\).
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Kallus, Y., Elser, V. & Gravel, S. Dense Periodic Packings of Tetrahedra with Small Repeating Units. Discrete Comput Geom 44, 245–252 (2010). https://doi.org/10.1007/s00454-010-9254-3
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DOI: https://doi.org/10.1007/s00454-010-9254-3