Archimedean frameworks

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. 

Smith, J.V. and Bennett, J.M. (1981) Enumeration of 4-connected 3-dimensional nets and classification of framework silicates the infinite set of ABC-6 nets the Archimedean and. sigma.-related nets. Am. Mineral., 66 (7-8), 777-788. 

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. 

Buckminsterfullerene. an allotrope of carbon, is topologically equivalent to a truneated ieosahedron, an Archimedean solid based on 12 pentagons and 20 hexagons (Fig. 5c).Eaeh earbon atom of the framework corresponds to a vertex of the polyhedron. As a result, C o is held together by 90 eovalent bonds, the number of edges of the solid. 

Figure 11 Two chemical examples of generalized Archimedean polyhedra (a) M012 truncated tetrahedron and (b) truncated octahedron whose vertices are occupied by the carboxylate carbon atoms of the bridging ligands in a metal-organic framework (the spacers of the bridging ligands are omitted for clarity).

The Ho6Co2Ga structure has been found with seven RiCo2Ga compounds, where R = Tb, Dy, Ho, Er, Tm, Lu and Y (GIGY, 83). The Ho6Co2Ga structure is shown in fig. 83 in a projection along c. The Co atoms are in the centres of deformed Archimedean antiprisms of Ho atoms, the Ga atoms occupy the icosahedral and the cubical voids in the Ho atom framework. Transition-metal centred Archimedean... 

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