Icosahedron, numbering system

A derivative of B12H122 is the carborane, Bi0C2H12. Note that this species is neutral because each of the carbon atoms has one more electron than does the boron atom and can, therefore, replace a B-H unit in the structure. Because all the positions in an icosahedron are identical, there will be three isomers of Bi0C2H12 that differ in the location of the two carbon atoms in the structure. The positions in the icosahedral structure are identified using the numbering system shown in Figure 8.8. Therefore, the structures for the three isomers of... 

Fig. 14.16. Nanoscaled systems of the biosphere and of chemistry show the same topology schematic representation of the icosahedron spanned by the 12 centres of the (Mo)IVIo5 units of the M0132 type cluster (a) and of the satellite tobacco necrosis virus (STNV) with the triangulation number F = 1...

The fifth regular solid, the icosahedron, and other 5-connected systems are omitted from Table 3.7 because there are no 5-connected plane or 3D nets composed of polygons of one kind only. For coordination numbers greater than six only 3D nets are possible. Two aspects of 3D nets which are important in structural chemistry should be mentioned here they will be discussed in more detail later. 

Fullerenes - Compounds composed solely of an even number of carbon atoms, which form a cage-like fused-ring polycyclic system with twelve five-membered rings and the rest sLx-mem-bered rings. The archetypal example is [60]fullerene, where the atoms and bonds delineate a truncated icosahedron. The term has been broadened to include any closed cage structure consisting entirely of three-coordinate carbon atoms. [5]... 

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