California NanoSystems Institute
University of California, Los Angeles
S9, Auditorium A0
In biology, symmetric structures are common, as few instructions are sufficient for self-assembly. In mathematics, examples of highly symmetric structures include some convex equilateral polyhedra Platonic, Archimedean and rhombic and helices. Many of these are found in biology, including some viruses and protein complexes with icosahedral symmetry, the ferritin cage with octahedral symmetry, and some viruses as well as DNA with helical symmetry. However, in geometry, the word polyhedron requires planar faces. Thus, some structures in biology and chemistry including large fullerenes, the clathrin cages responsible for endocytosis in cells, and some viruses too have nonplanar faces and are simply cages. However, some cages with nonplanar faces can be converted to polyhedra. The difference, cage versus polyhedron, may have functional consequences.