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arXiv · 0910.5226

Dense periodic packings of tetrahedra with small repeating units

Yoav Kallus·Veit Elser·Simon Gravel
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Abstract

We present a one-parameter family of periodic packings of regular tetrahedra, with the packing fraction $100/117\approx0.8547$, 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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Yoav Kallus, Veit Elser, Simon Gravel. 2010-03-19. Dense periodic packings of tetrahedra with small repeating units. https://doi.org/10.1007/s00454-010-9254-3

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