Archimedean solids snub cube

Fig. 9.2 (a) X-ray crystal structure of 1 and (b) the snub cube, one of the 13 Archimedean solids. The square faces of the snub cube correspond to the resorcin[4]arenes the eight shaded triangles that adjoin three squares correspond to the water molecules of 1. 

Fig. 9.9 The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), Cuboctahedron (2), Truncated cube (3), Truncated octahedron (4), Rhombicubocta-hedron (5), Snub cube (6), Icosidodecahedron (7),...

In addition to the Platonic solids, there exists a family of 13 convex uniform polyhedra known as the Archimedean solids. Each member of this family is made up of at least two different regular polygons and may be derived from at least one Platonic solid through either truncation or twisting of faces (Figure 3, Table 2). In the case of the latter, two chiral members, the snub cube and the snub dodecahedron, are realized. The remaining Archimedean solids are achiral. 

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,... 

In the XYj/ and XYj3 structures the X atoms occupy holes in which they are surrounded by 22 and 24 Y atoms respectively. For a given Y atom the smaller X metals form the XYx 1 phase and the larger ones the XYj 3 phase, while if X is too large even the XYj 3 phase is not formed (Table 29.8). This XY13 structure is of particular interest on account of the coordination polyhedra. The X atom has 24 Y neighbours at the vertices of a nearly regular snub cube, which is one of the less familiar Archimedean solids and has 6 square faces parallel to those of a cube and... 

Consultation of polyhedron models revealed the structure of 1 to conform to a snub cube, one of the 13 Archimedean solids, in which the vertices of the square faces correspond to the comers of 2 and the centroids of the eight triangles that adjoin three squares correspond to the eight water molecules. Indeed, to us, the ability of six resorcin[4]arenes to self-assemble to form 1 was reminiscent of spherical viruses in which identical copies of proteins self-assemble, by way of noncovalent forces, to form viral capsids having icosahedral symmetry and a shell-like enclosure. In fact, owing to the fit displayed by its components, 1 exhibits a topology that agrees with the theory of vims shell stmcture which states that... 

Fig. 5 Spherical hosts based on the Archimedean solids (a) metal-organic cage (truncated tetrahedron), (b) calix[4]resorcinarene spheroid (snub cube), and (c) buckminsterfullerene (truncated icosahedron). (View this art in color at www.dekker.com.)...

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