Archimedean solid geometry

Typically, synthetic capsules have a contained volume in the range 200-350 A3. In 1997, we discovered a spherical assembly consisting of [(C-methylresorcin[4]arene)6 (H20)8], 1. This assembly, Figure 1, with an enclosed volume of 1375 A3, was characterized by a single-crystal X-ray diffraction study and was found to be stable in nonpolar solvents [25]. Supramolecular assembly 1 ultimately led to the discovery of the link between 1 and the solid geometry principles of Plato and Archimedes [26], Before this discussion progresses, it is useful to examine briefly Platonic and Archimedean solids. 

We were also able to link the spherical assembly to the Archimedean solid known as the snub cube, Table 2. In a recent review, we have set forth structural classifications and general principles for the design of spherical molecular hosts based, in part, on the solid geometry ideas of Plato and Archimedes [27]. Indeed,... 

Metal triangles, tetrahedra, and octahedra form the basic building blocks of transition metal carbonyl clusters. The smaller clusters with between three and six metal atoms often adopt these pseudo-spherical deltahedral geometries, but as the nucle-arity of the cluster increases, condensed structures, built up from the smaller poly-hedra by vertex-, edge-, or face-sharing, tend to be favored in preference to the larger spherical deltahedra based on the Platonic and Archimedean solids. In general, this is in contrast to the structures foimd in borane chemistry. 

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