Periodic Borromean rings, rods and chains

This article describes periodic polycatenane structures built from interlocked rings in which no two are directly linked. The 2‐periodic vertex‐, edge‐ and ring‐transitive families of hexagonal Borromean rings are described in detail, and it is shown how these give rise to 1‐ and 3‐periodic ring‐transitive (isonemal) families. A second isonemal 2‐periodic family is identified, as is a unique 3‐periodic Borromean assembly of equilateral triangles. Also reported is a notable 2‐periodic structure comprising chains of linked rings in which the chains are locked in place but no two chains are directly interlinked, being held in place as a novel `quasi‐Borromean' set of four repeating components. The synthesis of molecular Borromean rings and other links is an active area of chemical research. Hypothetical 1‐, 2‐ and 3‐periodic molecular structures are described with the Borromean property that, although no two rings or chains are linked, the structures are interlocked and do not fall apart.