Discrete & Computational Geometry

, Volume 44, Issue 2, pp 245-252

First online:

Dense Periodic Packings of Tetrahedra with Small Repeating Units

  • Yoav KallusAffiliated withLaboratory of Atomic and Solid-State Physics, Cornell University Email author 
  • , Veit ElserAffiliated withLaboratory of Atomic and Solid-State Physics, Cornell University
  • , Simon GravelAffiliated withDepartment of Genetics, Stanford University School of Medicine

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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 \(\frac{139+40\sqrt{10}}{369}\approx0.7194\).


Packing Hilbert problem Crystallography Polyhedra Regular solid