Deltahedra most spherical

In 1971, a note 164) was published favoring the hypothesis that the carboranes, boranes, their isoelectronic anions, Lewis base adducts, and heteroatom-substituted analogs should be viewed as constructed about the vertices of either the most spherical series of triangular-faceted polyhedra (deltahedra) found to be characteristic of the dicarba-cZoao-carboranes (Fig. 1) or, with one lone exception, fragments of the series of deltahedra produced by the successive removal of the highest coordinated vertices that sequentially define the nido and arachno classes. This position was in conflict with the then prevalent shibboleth that all nido and arachno compounds [except B5H9 (I-N5)] had or would prove to have icosahedral fragment structures. 

The rules in overall decreasing order of importance essentially state that the ideal structures for carboranes will be based on most spherical deltahedra (rule 1) the BE hydrogens will tend to be placed in the lowest possible coordination environments (rule 2) when elements to the right of boron in the periodic table are incorporated into the deltahedron or deltahedral fragment, they will tend to preempt low-coordination sites (e.g., carbon) or, if electron-deficient, high coordination sites (rule 3) and, lastly, boron will eschew seven-coordinate BH or six-coordinate... 

Figure 2 The most spherical deltahedra, found, for example, in the structures of the boranes (6 < n < 12). The numbers on the...

A polyhedron with e edges has e distinct dsd situations if at least one of these dsd situations is degenerate by satisfying Equation (1.10), then the polyhedron is inherently fluxional [40]. The inherent rigidity/fluxionality of the most important deltahedra including the most spherical deltahedra found in boranes (Figure 1.4) is summarized in Table 1.1. 

The experimentally observed metallaborane deltahedra are related to the most spherical deltahedra by a series of one or more dsd processes [62,63]. For example, among the 10-vertex deltahedra a single dsd process converts the most spherical bicapped square antiprism (Figure 1.4) of four-fold D d symmetry found in BioHio to a deltahedron of three-fold Csv symmetry with a single degree 6 vertex (Figure 1.11a). The square intermediate in this single... 

Figure 3. The most spherical deltahedra found in the boranes (6 < / < 12) and related compounds.

Fig. 1-2. The most nearly spherical deltahedra found in the boranes B H 2 (6 < n < 12) and isoelectronic carboranes.

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