Virus capsids are highly specific assemblies that are formed from a large number of often chemically identical capsid subunits. In the present paper we ask to what extent these structures can be viewed as mathematically tilable objects using a single two-dimensional tile. We find that spherical viruses from a large number of families-eight out of the twelve studied-qualitatively possess propert...

The Platonic multiverse view is that there are multiple and incompatible concepts of a set with corresponding Platonic universes. For example the continuum hypothesis may be true in some of these universes and false in others. This philosophical view leads to an approach for exploring mathematics that is similar to an approach that stems from the more conservative view that infinity is a potent...

The problem of classifying, up to isometry, the orientable spherical and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. This allows us to complete the classification begun by Best [Canad. J. Math. 23 (1971) 451], Lorimer [Pacific J. Math. 156 (1992) 329], Richardson and Rubinstein [Hyperbolic manifolds from a regul...