A sphere packing slideshow

We have enumerated all the ways to arrange n <= 13+ spheres as a cluster that is nonlinearly rigid. We have discovered many packings that are hypostatic, namely they have fewer than the 3n-6 contacts required to be linearly rigid. Simple scaling arguments explain why these are thermodynamically important when the spheres are colloids interacting with a short-range potential. We discuss these clusters, as well as other surprises that came up along the way. ("+" means we have enumerated only a particular kind of cluster for n=14, 15, and beyond.)