Why the Platonic and Archimedean Solids

With interests in chemical synthesis moving towards the fabrication of nanometer scale molecular frameworks [6, 47-49] and the miniaturization of functional micro- 

the Platonic and Archimedean solids not only provide a means for host design, but a way in which to maximize chemical information, allowing the chemist to simplify the structures of complex molecular frameworks and, in effect, engineer host-guest systems. 

Using information obtained from X-ray crystallography, we have described the structure of a chiral, spherical molecular assembly held together by 60 hydrogen bonds. [10] The host, which conforms to the structure of a snub cube, self-assembles in apolar media and encapsulates guest species within a cavity that possesses an internal volume of approximately 1.4 nm3. 

From this information, general principles for the design of spherical molecular hosts have been developed. [11] These principles rely on the use of convex uniform polyhedra as models for spheroid design. To demonstrate the usefulness of this approach, structural classification of organic, inorganic, and biological hosts - frameworks which can be rationally compared on the basis of symmetry - has revealed an interplay between symmetry, structure, and function. [53] 

Indeed, we anticipate that the Platonic and Archimedean solids may be used for the construction of hosts which conform to those solids not yet realized and additional members of each family, where supramolecular synthesis, via self-assembly, will play a major role in their design, ushering in an era of spherical host-guest chemistry. 

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