Entanglement by design: Symmetry-guided periodic helical assemblies

TL;DR

This paper presents symmetric three-periodic tangled nets and filaments constructed via crystal nets with helical windings, offering insights into their organization in various systems.

Contribution

It introduces a collection of symmetric, periodic tangled structures built from crystal nets, emphasizing recurring geometric motifs without full classification.

Findings

Highlights geometric motifs in periodic tangles

Demonstrates construction via crystal nets and helical windings

Provides insight into organization in crystalline and biological systems

Abstract

In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments are 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 insight into how periodic tangles are organised in crystalline, molecular, and biological systems.