From viruses to fullerene molecules

Abstract

What do the surface structure of viruses, the morphology of sea radiolaria, the pattern on a golf ball, the weaving of baskets, the geodesic dome structure of Buckminster Fuller, the sewing design on a soccer ball and the C₆₀ fullerene molecule all have in common? The feature common to all these and many other phenomena is a family of structures displaying a characteristic symmetry: truncated icosahedra. Truncated icosahedral structures belong to the sizeable set of polyhedra invariant under spatial rotations. It is no accident that a similar structure developed. Their formation involved a common principle of structure construction, that of so-called synergy.