Platonic shells

Three or more molecules may assemble in the solid state to form a finite assembly with connecting forces propagated in 3D. The components of such an assembly will typically form a polyhedral shell. The shell may accommodate chemical species as guests. The polyhedron may be based on a prism or antiprism, as well as one of the five Platonic (e.g. cube, tetrahedron) or 13 Archimedean (e.g. truncated tetrahedron) solids.4... 

With interests in chemical synthesis moving towards the fabrication of nanometer-scale molecular frameworks " and the miniaturization of functional microstruc-tures (Scheme 2), it becomes apparent why the Platonic and Archimedean solids are appropriate models for shell design. 

It has been proposed to call the Mon i2-type cluster a Keplerate corresponding to Kepler s early speculative model of the cosmos and concept of planetary motion, as described in his opus Mysterium Cosmographicum [10]. In accordance with this model, Kepler believed that the distances between the orbits of the planets could be explained if the ratios between the successive orbits were designed to be equivalent to the spheres successively circumscribed around and inscribed within the five Platonic solids. By analogy, the cluster correspondingly shows concentric spherical shells of 132 terminal oxygen and 132 molybdenum atoms while the centers of the 12 [(Mo)°(Mo5) ... 

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