Icosahedral clusters boron allotropes

The /3-R105 boron allotrope has a much more complex structure with 105 B atoms in the unit cell (space group R3m, a = 1014.5 pm, a = 65.28°). A basic building unit in the crystal structure is the B84 cluster illustrated in Fig. 13.2.5(a) it can be considered as a central Bi2a icosahedron linked radially to 12 B6 half-icosahedra (or pentagonal pyramids), each attached like an inverted umbrella to an icosahedral vertex, as shown in Fig. 13.2.5(b). 

Elementary boron exists in the solid state in several allotropic forms. Those which have been properly characterized by X-ray diffraction contain icosahedral B12 units, which are also the basis of many boron cluster compounds. 

The uniqueness of boron is clearly seen in its elemental forms, the number and structural complexity of which exceed those of any other element. At least five distinct allotropes are known, all of which contain icosahedral B12 cluster units that in most cases are accompanied by other boron atoms lying outside the icosahedral cages. The most thermodynamically stable form, j8-rhombohedral boron, has 105 B atoms in its unit cell, while the /3-tetragonal phase has 192 atoms and is still not completely elucidated despite years of study ... 

In most of its allotropic forms, elemental boron exists in Bi2 icosahedral structural units. An icosahedron has 12 vertices and 20 faces, each of which is a triangle. The manner in which the B12 clusters are Unked together to produce a large three-dimensional network accounts for the high melting point and extreme hardness of this element. 

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