Deltahedron parent

Series Parent Formula Skeletal Electrons Cluster Geometry (deltahedron = closed triangulated polyhedron)... 

The sep = 9 = n + 1 n = 8. Removing two adjacent five-connect vertices from the parent deltahedron (four four-connect and four five-connect vertices) yields the framework shown (as well as flattened out for convenience at the bottom left) which has C2 symmetry (pairwise equivalence of Bs and Hs) and therefore consistent with the observed spectroscopic data. 

The structural patterns illustrated in Figure 3.1, and the shapes shown in column 3 for arachno species, are essentially those first suggested by Williams in 1971,2 and have stood the test of time remarkably well. However, the shapes shown should be regarded as illustrative rather than definitive. As with the nido species, alternative shapes to those shown in Figure 3.1 are possible for arachno species, with different sites left vacant on the parent deltahedron. We have already noted that many nido boranes and carboranes with eight skeletal atoms show deviations in their atom connectivities from those shown in Figure Nevertheless, apart from these particular exceptions,... 

Number of Skeletal Electron Pairs" Parent Deltahedron (Symmetry) Closo Species CjB,H,+2 (H ) Nido Species C,B,H,44 (H"), Arachno Species C3,H + (H ),... 

The number of skeletal electron pairs exceeds the number of vertices on the parent deltahedron by one. Benzvalene. 

The total number of electrons corresponds to (n + 1) pairs of electrons, and thus, the number of vertices, n, of the parent deltahedron can be established. 

Each BH -unit occupies one vertex in the parent deltahedron, and from the number of vertices left... 

The parent deltahedron is an octahedron and the B5-core of [BsHg] will be derived from an octahedron with one vertex left vacant ... 

This corresponds to a monocapped structure, the parent deltahedron being one with 5 vertices, i.e. a trigonal bip5Tamid ... 

Each BH -unit occupies one vertex in the parent deltahedron, and from the number of vertices left vacant, the class of cluster can be determined if vertices are nonequivalent, the first to be left vacant tends to be either one of highest connectivity or a cap in capped structures (e.g. H = 9 and 10 in Figure 13.27). 

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