Spontaneous self-assembly processes that lead to discrete spherical molecular structures are common in nature. Spherical viruses’ (such as hepatitis B) and fullerenes(2) are well-known examples in which non-covalent and covalent forces, respectively, direct the assembly of smaller subunits into larger superstructures. A common feature of these shell-like architectures is their ability to encapsulate neutral and/or charged guests whose size, shape and chemical exteriors complement those of the host’s inner surface(3,4). Their interiors can often be regarded as a new phase of matter(5), capable of controlling the flow of reactants, transients and products, and of catalysing reactions of both chemical and biological relevance. Such properties have inspired the recent emergence of monomolecular(5-7) and supramolecular dimeric molecular capsules(8,9), many of which have been based on the head-to-head alignment of bowl-shaped polyaromatic macrocycles such as calix[4]arenes(5,7,9). But true structural mimicry of frameworks akin to viruses and fullerenes, which are based on the self-assembly of n > 3 subunits, and where surface curvature is supplied by edge sharing of regular polygons, has remained elusive. Here we present an example of such a system : a chiral spherical molecular assembly held together by 60 hydrogen bonds (1) (Fig, 1). We demonstrate the ability of 1, which consists of six calix[4]resorcinarenes 2 and eight water molecules, to self-assemble and maintain its structure in apolar media and to encapsulate guest species within a well-defined cavity that possesses an internal volume of about 1,375 Angstrom(3). Single crystal X-ray analysis shows that its topology resembles that of a spherical virus(1) and conforms to the structure of a snub cube, one of the 13 Archimedean solids(10).