Close-packing rules may not guide nanoparticle self-assembly after all

Three-dimensional shapes fill physical space in a certain way. If you pour marbles into a jar, the marbles will randomly pack within the jar. If you carefully placed every marble, layer-by-layer in the jar such that the marbles in one layer sit within the crevices between marbles on the layer below it, you can pack a few more marbles in the jar than if it was randomly packed. This will give you the highest density packing, or the least amount of space between particles.