Abstract
This chapter discusses developments in finite packing and explains covering problems with special emphasis on problems involving convex bodies. What sausage packing and bin packing problems have in common is that convex bodies are packed into a convex body of the smallest possible volume among all bodies of a given family. Sausage covering problems fall into a corresponding category. The volume of a polytope can be computed in polynomial time. There is a close relation between lattice point problems and lattice packing and covering. Unlike the usual lattice-like 3-dimensional atomic growth of metals, under certain conditions, some metals develop whiskers—microscopic filaments of a certain maximum length. For chemical reasons, molecular growth is constrained to subsets of specific lattice packings.
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