Closo Carboranes skeletal shapes

Because of their completely deltahedral pseudospherical shapes, the dianions, the singly charged monocarbaborane anions [CB iH ], and the neutral carboranes of formulae C2B 2H are known as closo (closed cage) clusters. Their skeletal shapes are shown in the left-hand column of Figure 3.1. 

Figure 3.1. Deltahedral and deltahedral fragment skeletal shapes of typical closo, nido, and arachno boranes and carboranes.

Figure 3.25. Some of the skeletal shapes found for large carboranes and metallacarboranes, showing connectivities of four or six in closo systems.

H. C. Longuet-Higgins and M. de V. Roberts, who predicted thereby that the icosahedron of 12 boron atoms familiar from elemental boron, boron carbide, and some borides should be stabilized in molecular hydride form, not as the neutral entity B Hu (which if icosahedral would be a diradical) but as the dianion [B12H12] , which contained the 25 valence shell electron pairs needed for the 12 exo B-H bonds and 13 skeletal bonding MOs. Subsequent MO treatments of the closo deltahedral anions B I 1 and carboranes (AB, 2H, in Figure 3.1 have shown that these are the shapes that make best bonding use of their (n + 1) pairs of electrons available for skeletal bonding. ... 

---