Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra

@article{HajiAkbari2009DisorderedQA,
  title={Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra},
  author={Amir Haji-Akbari and Michael Engel and Aaron S. Keys and Xiaoyu Zheng and Rolfe Petschek and Peter Palffy-Muhoray and Sharon C. Glotzer},
  journal={Nature},
  year={2009},
  volume={462},
  pages={773-777}
}
All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of φ = π/√18 ≈ 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with φ = 0.7786 (ref. 4), which was subsequently compressed numerically to φ = 0.7820 (ref. 5), while compressing with different… 
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