From untangled graphs and nets to tangled materials
Stephen T. Hyde
, a, 
and Olaf Delgado Friedrichsa
Received 13 April 2010;
revised 19 October 2010;
accepted 21 October 2010.
Available online 11 November 2010.
Abstract
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.
Graphical abstract
Tangled nets offer a new class of material structure, often combining chirality and high porosity.
