Building polyhedra by self-assembly

Models of the Platonic and Archimedean solids may be found in many mathematics classrooms. Important examples of polyhedra in nature are the fullerenes in chemistry and icosahedral viral capsids in biology. Such polyhedra "self-assemble" from their constituent atoms or proteins. In the past few years, an exciting development in science has been the use of self-assembly as a strategy to build devices and containers on very small scales. These experiments raise some interesting mathematical questions. I will describe our work on "self folding" polyhedra and various questions on the combinatorics of assembly pathways.

This work is in collaboration with several students and David Gracias's lab at Johns Hopkins.