Abstract:

Since the discovery of molecule of C60 (truncated icosahedron), fullerenes, i.e., simple polyhedra with only pentagonal and hexagonal faces, became the main object in Organic Chemistry; the synthesis of C60 was marked by the Nobel prize 1996. Crick and Watson.s article in Nature, 10-3-1956, starts: "It is a striking fact that almost all small viruses are either rods or spheres". In fact, all virions, except most complex, as brick-like pox virus, and some enveloped ones, are helical or (about half of all and almost all human) icosahedral: dual fullerenes with Ih or chiral I symmetry.

Caspar and Klug, Nobel prize 1982, gave quasi-equivalence principle: virion minimizes by organizing capsomers in minimal number of locations with noneqvuivalent bonding, resulting in icosadeltahedral (dual icosahedral fullerene) structure.

We give an up to date survey on geometries of virion capsids and related mathematics. It will be an expositary lecture