FIGURE 1. Two-dimensional view of packings.

From the following article:

Mathematical physics: A tight squeeze

Henry Cohn

Nature 460, 801-802(13 August 2009)

doi:10.1038/460801a

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a, In a two-dimensional Bravais lattice packing, there is one particle per lattice cell, and the particles are all aligned with each other. In this illustration, the particle is represented by a triangle and is located in the upper left corner of the cell. b, In a general, non-Bravais lattice packing, there are multiple particles per cell, and they can be arbitrarily rotated. In their computer simulations, Torquato and Jiao1 show that the best packings of centrally symmetric Platonic solids turn out to be Bravais lattice packings, which is remarkable given how restricted such packings are.

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