Regular deltahedra

Most of the structures of metallacarbaborane clusters derive from triangular-faced polyhedra. Figure 1 shows regular deltahedra up to the icosahedron with the corresponding lUPAC vertex numbering schemes. General cluster classes are closo (a complete deltahedral structure), nido (a deltahedron with one vertex vacant), arachno (a deltahedron with two... 

The structure of most known boranes and carboranes are based on the regular deltahedra illustrated in Fig. 2.27. Three types of structures are known for this class of compounds closo (closed), nido (nest-like) and arachno-stvuc-tures ( cobweb structures). The relationship between these three types of... 

Fig. 2.27. Regular deltahedra often found in molecular structures of boranes and carboranes. (a) Tetrahedron (b) trigonal bipyramid (c) octahedron (d) pentagonal bipyramid (e) dodecahedron (f) tricapped trigonal prism (g) bicapped archimedean antiprism (h) octahedron (i) icosahedron...

In accord with and in addition to Plato s view of convex polyhedra, there is only a limited number of polyhedra, regular or irregular, mostly more or less distorted, that are observed as cluster polyhedra, mostly deltahedra. 

Boron hydrides and carboranes adopt structures in which their skeletal boron and/or carbon atoms form complete or nearly complete deltahedra, i.e. regular polyhedra with triangular faces. 

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