Polyhedron Model - Snub Cube

The discovery that members of the resorcin[4]arene family self-assemble to form 1, owing to its classification as an Archimedean solid, prompted us to examine the topologies of related spherical hosts with a view to understanding their structures on the basis of symmetry. In addition to providing grounds for classification, we anticipated that such an approach would allow us to identify similarities at the structural level, which, at the chemical level, may not seem obvious and may be used to design large, spherical host assemblies similar to 1. 

it is herein that we now describe the results of this analysis which we regard as the development of a general strategy for the construction of spherical molecular hosts. [11] We will begin by presenting the idea of self-assembly in the context of spherical hosts and then, after summarizing the Platonic and Archimedean solids, we will provide examples of cubic symmetry-based hosts, from both the laboratory and nature, with structures that conform to these polyhedra. 

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Consultation of polyhedron models revealed the structure of 1 to conform to a snub cube, one of the 13 Archimedean solids, in which the vertices of the square faces correspond to the comers of 2 and the centroids of the eight triangles that adjoin three squares correspond to the eight water molecules. Indeed, to us, the ability of six resorcin[4]arenes to self-assemble to form 1 was reminiscent of spherical viruses in which identical copies of proteins self-assemble, by way of noncovalent forces, to form viral capsids having icosahedral symmetry and a shell-like enclosure. In fact, owing to the fit displayed by its components, 1 exhibits a topology that agrees with the theory of vims shell stmcture which states that... 

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