Tori in dichten gitterförmigen Kugelpackungen. (Tori in dense lattice packings of balls) (Q1091613)

Consider a lattice packing of balls of unit radius in \({\mathbb{R}}^ 3\) of maximum density. Circular tori can be embedded in different ways into the part of space not covered by the balls. The author describes four topologically different ways for such embeddings and shows that they are (topologically) the only embeddings for which the central circles are parallel to lattice planes containing regular lattice triangles or squares. It is an open problem to describe the topologically distinct types of embeddings of tori with no assumptions about the position of the central circle.