On the Optimality of the FCC Lattice for Soft Sphere Packing

@article{Edelsbrunner2018OnTO,
  title={On the Optimality of the FCC Lattice for Soft Sphere Packing},
  author={Herbert Edelsbrunner and Mabel Iglesias Ham},
  journal={SIAM J. Discret. Math.},
  year={2018},
  volume={32},
  pages={750-782}
}
Motivated by biological questions, we study configurations of equal spheres that neither pack nor cover. Placing their centers on a lattice, we define the soft density of the configuration by penalizing multiple overlaps. Considering the 1-parameter family of diagonally distorted 3-dimensional integer lattices, we show that the soft density is maximized at the FCC lattice. 
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