Dense periodic packings of tetrahedra with small repeating units

Details Dense periodic packings of tetrahedra with small repeating units Dense periodic packings of tetrahedra with small repeating units

2009-10-27

arxiv.org/abs/0910.5226v5

Discrete and Computational Geometry, 2010

Mathematics

Metric Geometry

Last draft submitted for publication. Published version available at http://www.springerlink.com

Scientific paper

10.1007/s00454-010-9254-3

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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