Periodic Borromean rings, rods and chains

Abstract

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.