(A) Stacking of spheres as in an lattice. In this densest lattice in 3D, each sphere touches 12 other spheres and there are four different planar hexagonal lattices through each node. (B) Over a layer of hexagonally arranged spheres centered at γ0 (in black) one can put another hexagonal layer by starting from one of six locations, two of which are highlighted, γ1 and γ2. (C) If one arranges the hexagonal layers according to the sequence (…,γ1, γ0, γ2,…) one obtains the . Note that spheres in layer I are not aligned with those in layer III. (D) Arranging the hexagonal layers following the sequence (…,γ0, γ1, γ0,…) leads to the hexagonal close packing . Again, each sphere touches 12 other spheres. However, there is only one plane through each node for which the arrangement of the centers of the spheres is a regular hexagonal lattice. This packing has the same packing ratio as the , but is not a lattice. (E) for bump-function Ω with and for various parameter combinations θ1 and θ2; θ1 modulates the decay and θ2 the support. The two packings have the same packing ratio and for this tuning curve also provide identical spatial resolution. FI: Fisher information.