On the Optimality of the FCC Lattice for Soft Sphere Packing
Herbert Edelsbrunner, Mabel Iglesias-Ham · SIAM Journal on Discrete Mathematics · 2018
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.