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# Dense Periodic Packings of Tetrahedra with Small Repeating Units

Discrete & Computational Geometry, 2010 Sep, Vol.44(2), pp.245-252 [Peer Reviewed Journal]

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• Title:
Dense Periodic Packings of Tetrahedra with Small Repeating Units
• Author: Kallus, Y ; Elser, V ; Gravel, S
• Found In: Discrete & Computational Geometry, 2010 Sep, Vol.44(2), pp.245-252 [Peer Reviewed Journal]
• Subjects: Mathematics - Metric Geometry ; Condensed Matter - Soft Condensed Matter ; Condensed Matter - Statistical Mechanics
• Language: English
• Description: 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 $\frac{139+40\sqrt{10}}{369}\approx0.7194$. Comment: Last draft submitted for publication. Published version available at http://www.springerlink.com
• Identifier: ISSN: 0179-5376 ; DOI: 10.1007/s00454-010-9254-3