The geometry of periodic knots, polycatenanes and weaving from a chemical perspective: a library for reticular chemistry

The geometry of simple knots and catenanes is described using the concept of linear line segments (sticks) joined at corners. This is extended to include woven linear threads as members of the extended family of knots. The concept of transitivity that can be used as a measure of regularity is explained. Then a review is given of the simplest, most regular 2- and 3-periodic patterns of polycatenanes and weavings. Occurrences in crystal structures are noted but most structures are believed to be new and ripe targets for designed synthesis. The geometry of the most regular polycatenanes and weavings, as an extended family of discrete knots and catenanes, is described in terms of sticks and corners in their optimal embeddings.