In the early 2000s, while thinking about the Penrose tiling and different ways of dividing the surface of a sphere, Twarock created a model describing the exceptional structure of papovaviridae. Almost all icosahedral viruses have proteins on their capsids arranged in clusters of five and six, with a structure permitting at most 12 clusters of five, but papovaviridae, including HPV, have 72 clusters of five This protein layout did not correspond to any spherical polyhedron known to mathematics.
