The Beauty of Topological Defects in Materials Science, Art, and Design*

Topological defects play a starring role in materials science, controlling everything from the bending of metal to the solidification of polymers. While defects represent disruption in an ordered pattern, surprisingly they can sometimes enhance material properties. Patterns on curved or closed surfaces typically require defects, as exemplified by the mix of black-and-white shapes on a soccer ball. Inspired by those fundamental geometric principals, I helped organize a team of visitors at the KITP in Santa Barbara to design a “topology dress” composed of hexagons, pentagons, and heptagons. These were strategically combined in a patchwork to match a mannequin’s shape with regions of positive and negative Gaussian curvature. We’ll look at topological defects also in the context of other examples of art and design, and their analogs in the science of hard and soft materials.