From untangled graphs and nets to tangled materials

We suggest constructive definitions for the determination of untangled finite graphs and three-periodic nets, using barycentric embeddings in two and three dimensions. The possibility of deliberately constructing tangled graphs and nets is canvassed, and we conclude that tangled patterns offer a novel class of nano- and meso-structured materials with useful features, including high internal surface area and volume and chirality.

Tangled nets offer a new class of material structure, often combining chirality and high porosity. Figure optionsDownload as PowerPoint slide