Papillomaviridae were therefore the first known exception to "quasi-equivalence theory", which essentially holds that virus capsids resemble goldberg polyhedra. In fact, the protein layout on papillomaviridae turned out not correspond to any known spherical polyhedron, so their structure was an open question for more than two decades. The question was eventually answered in 2003 by Reidun Twarock, using a model based on the Penrose tiling[30] with two proteins in a dimer taking the place of a rhombus and three proteins in a trimer taking the place of a kite.