Icosadeltahedral geometry of fullerenes, viruses and geodesic domes

Abstract

I discuss the symmetry of fullerenes, viruses and geodesic domes within a unified framework of icosadeltahedral representation of these objects. The icosadeltahedral symmetry is explained in details by examination of all of these structures. Using Euler's theorem on polyhedra, it is shown how to calculate the number of vertices, edges, and faces in domes, and number of atoms, bonds and pentagonal and hexagonal rings in fullerenes. Caspar-Klug classification of viruses is elaborated as a specific case of icosadeltahedral geometry.