Sphere Packing

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Sphere packing problems treat the general question of how (often identical) spheres can be arranged in a given space without overlapping. In mathematics, problems of this type have a long and rich history. One of the most famous versions of this general type of questions is the Kissing number problem.

While the natural choice for the space in which the sphere packing takes place is three dimensional Euclidean space, it can be generalized to any n-dimensional space, with Euclidean or non-Euclidean geometry. The most commonly studied of these generalizations is two dimensional space, where spheres are circles, because it is much simpler to represent and most of the complexity of the original problem is preserved. An especially entertaining representation are the puzzles of the type designed by Bill Gosper like the Troublesome Twelve.

The packing of spheres into a given volume is also a common problem in many areas of physics. In the context of soft matter, self-assembly is one of the most prominent ones. An example where the uniqueness of a certain class of packings is used to explain phenomena in self assembly is the paper Evaporation Driven assembly of colloidal particles.