Spontaneous self-assembly processes that lead to discretespherical molecular structures are common in nature. Sphericalviruses1 (such ashepatitis B) and fullerenes2 are well-known examples inwhich non-covalent and covalent forces,respectively, direct the assembly of smaller subunits intolarger superstructures. A common feature of theseshell-like architectures is their ability to encapsulateneutral and/or charged guests whose size, shape and chemicalexteriors complement those of the host's innersurface3,4. Their interiors can often beregarded as a new phase of matter5, capable of controlling the flowof reactants, transients and products, and of catalysingreactions of both chemical and biological relevance. Suchproperties have inspired the recent emergence ofmonomolecular5,6,7 and supramolecular dimeric molecularcapsules8,9, many of which have been basedon the head-to-head alignment of bowl-shapedpolyaromatic macrocycles such as calix[4]arenes5,7,9. But true structural mimicry offrameworks akin to viruses and fullerenes, which are based onthe self-assembly of n > 3 subunits,and where surface curvature is supplied by edge sharing of regularpolygons, has remained elusive. Here we present anexample of such a system: a chiral spherical molecular assemblyheld 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 A3. Single crystal X-ray analysis shows that its topology resembles that of a spherical virus1 and conforms to the structure of a snub cube, one of the 13 Archimedean solids10.