Entanglement by design: symmetry-guided periodic helical assemblies

Abstract In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments is presented. They are constructed via familiar crystal nets using edges as geometric scaffolds for n-fold helical windings. Rather than providing a complete classification, this gallery of examples highlights recurring geometric motifs, offering insights into how periodic tangles are organized in crystalline, molecular and biological systems. This article is part of the theme issue ‘Geometry, materials and the imagination’.