Rhombicuboctahedron

Muller et al. have shown that 24 oxygen atoms of the polyoxometalate [As4Mo6V7039]2- may be attributed to the structure of a rhombicuboctahedron. [44] Notably, a strong tetrahedral distortion of each ion is required to correspond each host to the polyhedron. This shell has been shown to complex a sulfate ion in the solid state. 

In the above sections examples of the snub cube, the great rhombicuboctahedron, and the small rhombicuboctahedron have been presented. The guests are badly disordered for all of the capsules except for that made from p-sulfonatocalix [4]arene anions, pyridine V-oxide, and lanthanide ions. 

Plate 22 (Figure 3.12). (a) he spherical capsule consisting of six pyrogallol[4]arene molecules shown in the capped-stick metaphor, and (b) with the carbon and hydrogen atoms removed. Hydrogen bonds are shown as thin, solid red lines. Parts (c) and (d) show the remarkable correspondence of the hydrogen bonded pattern with the Archimediean solid, the small rhombicuboctahedron. 

Figure 2.5 The great rhombicuboctahedron of 48 vertices and 72 edges, formed as the union of 12 square faces, 6 octagons and 8 hexagons. Vertices of the polyhedron are coloured in sets of 8, 6 and 4 to identify the face types present, the centres of which correspond to axes of proper rotation of the point.

Figure 2.10 The results of pairwise contractions of the vertices of the octagons surrounding the four-fold axes of the regular orbit cage, using the colour coding of Figure 2.7. The first choice of pairs to be contracted leads to the formation of the truncated octahedron, while the alternative choice gives rise to the small rhombicuboctahedron.

Figure 2.11 The results of pairwise contractions of the vertices of the hexagons of the regular orhit cage of 0[, symmetry, again with the colour coding as in Figure 2.7. The first pairing choice, column 1, leads to the 24-vertex cage of the truncated cube, while the second choice leads to a further copy of the small rhombicuboctahedron.

In Figure 2.14a, the 48-vertex structure of the great rhombicuboctahedron is divided into two sets of 24 points, coloured to distinguish two sets related by the inversion operation. Each set of 24 vertices now exhibit O symmetry and are examples of the chiral polyhedra based on the snub cube structure, displayed as the ri-isomer as a projection in Figure 2.14b and as a perspective drawing in Figure 2.14b. 

Figure 2.18 (a) The regular orbit of T[, symmetry as an elliptical projection and (b) in perspective displaying the structure as a modified small rhombicuboctahedron, in which there is no reflection symmetry across face diagonals of the inscribing cube. 

Figure 11. The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), cuboctahedron (2), truncated cube (3), truncated octahedron (4), rhombicuboctahedron (5), snub cube (6), icosidodecahedron (7), rhombi-truncated cuboctahedron (8), truncated dodecahedron (9), truncated icosahedron (10), rhombicosidodecahedron (11), snub dodecahedron (12), rhombitruncated icosidodecahedron (13) (see also Table 2).

Figure 13 A schematic of the two types of polyhedron formed by the Vig clusters. The Ta rhombicuboctahedron is shown on the LHS and the pseudorhombicuboctahedron is shown on the RHS.

Fig. 35. cont.) Paulingite. (b) A polyhedral representation of the one unit cell of the crystal structure [96B1, 10H2]. The nomenclature of cavities follows the original work grc is a great rhombicuboctahedron. (c) A complete scheme of cavities in the unit cell. Spheres correspond to the free volume of cavities channel diameters are proportional [10H2]. (cont.)... 

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