Platonic frameworks

Fig. 4.12 The Platonic frameworks (a) tetrahedron (b) cube (c) octahedron (d) dodecahedron (e) icosahedron.

Thus, 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. 

Molecular frameworks with the shapes of each Platonic solid are known. In symmetry terms, the Platonic solids split into two families the tetrahedron, the cube and the octahedron, which have cubic symmetry, and the icosahedron and the dodecahedron, which have icosahedral symmetry. 

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. 

The transition-metal clusters often display highly symmetrical metal frameworks, normally with symmetries derived from the platonic or archimedian solids or variations thereof. The post-transition element clusters, on the other hand, are not necessarily aflfected by such confinements. However, as will be explained in Sec. 1.29.4, relationships between the structure and the electron count do exist for the naked clusters, and regular, closed geometries are found for a rather large group of these species. For instance, the trigonal prismatic symmetry of the Rhf, framework in Fig. lA is also found in the naked tellurium cluster... 

Humans are twofold in nature mortal in body, but immortal in essence. Even though we are immortal, as long as we are bound in bodies we are subject to fate as the author of Poimandres makes clear, although humans are above the cosmic framework, they became slaves within it Poim. 15). This fundamental dualism—the direct heritage of Platonic thought—means that the body is fundamentally connected with sexual intercourse and the cycle of physical birth and death ... 

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