Icosahedron truncated

Fullerenes are described in detail in Chapter 2 and therefore only a brief outline of their structure is presented here to provide a comparison with the other forms of carbon. The C o molecule, Buckminsterfullerene, was discovered in the mass spectrum of laser-ablated graphite in 1985 [37] and crystals of C o were fust isolated from soot formed from graphite arc electrodes in 1990 [38]. Although these events are relatively recent, the C o molecule has become one of the most widely-recognised molecular structures in science and in 1996 the codiscoverers Curl, Kroto and Smalley were awarded the Nobel prize for chemistry. Part of the appeal of this molecule lies in its beautiful icosahedral symmetry - a truncated icosahedron, or a molecular soccer ball, Fig. 4A. 

Another contribution is represented by an investigation of a cubic thallium cluster phase of the Bergmann type Na13(TlA.Cdi A.)27 (0.24 < x <0.33) (Li and Corbett 2004). For this phase too the body centred cubic structure (space group Im 3, a = 1587-1599 pm) may be described in terms of multiple endo-hedral concentric shells of atoms around the cell positions 0, 0, 0, and 14,14,14. The subsequent shells in every unit are an icosahedron (formed by mixed Cd-Tl atoms), a pentagonal dodecahedron (20 Na atoms), a larger icosahedron (12 Cd atoms) these are surrounded by a truncated icosahedron (60 mixed Cd-Tl atoms) and then by a 24 vertices Na polyhedron. Every atom in the last two shells is shared with those of like shells in adjacent units. A view of the unit cell is shown in Fig. 4.38. According to Li and Corbett (2004), it may be described as an electron-poor Zintl phase. A systematic description of condensed metal clusters was reported by Simon (1981). 

Figure 5.36. Schematic representation of the fullerene C60 molecule. Notice its highly symmetric structure (truncated icosahedron) in which all carbon atoms are identical and are located at the connection between two hexagons and one pentagon. The bond lengths are 138.6 pm for the bonds common to two hexagons (having a double-bond resonant structure) and 143.4 pm for the hexagon-pentagon common bonds. The bonding therefore seems to be not completely delocalized as in graphite.

Rhombitruncated cuboctahedron (8), Truncated dodecahedron (9), Truncated icosahedron (10), Rhombicosidodecahedron (11), Snub dodecahedron (12), Rhombitruncated icosidodecahedron (13) (see also Table 9.2). 

Buckminsterfullerene, an allotrope of carbon, is topologically equivalent to a truncated icosahedron, an Archimedean solid that possesses 12 pentagons and 20 hexagons (Fig. 9-16). [17] Each carbon atom of this fullerene corresponds to a vertex of the polyhedron. As a result, C6o is held together by 90 covalent bonds, the number of edges of the solid. 

Fig. 9.16 X-ray crystal structure of buckminster-fiillerene, C6o, a shell based upon the truncated icosahedron.

Fullerenes (Ceo) (Fig- 3) have a structure similar to that of truncated icosahedron, made out of five- and six-member rings of sp carbons. Higher fullerenes are also made of five- and six-member carbon rings. 

This polymorph of carbon was only discovered in 1985 by Sir Harry Kroto at the University of Sussex while looking for carbon chains. It is made by passing an electric arc between two carbon rods in a partial atmosphere of helium. Kroto was awarded the Nobel Prize in chemistry in 1996, along with two American researchers (Robert F.Curl Jr. and Richard E.Smalley). The molecule has the formula Ceo and has the same shape as a soccer ball—a truncated icosahedron it takes its name from the engineer and philosopher Buckminster Fuller who discovered the architectural principle of the hollow geodesic dome that this molecule resembles (a geodesic dome was built for EXPO 67 in Montreal). The structure is depicted in Figure 6.14. 

BLCKM1NS l ERP LLLERENE (Buckyballs). C60. Spherical aromatic molecule willi a hollow truncated-icosahedron structure, similar to a soccer ball. First reported in the mid 1980s. Capable of enclosing ions or atoms in a host-guest relationship. See also Carbon Compounds. 

In tetragonal-50 boron (T-50) the B12 icosahedra are bonded by B—B bonds and B atom bridges. Lattice constants vary from specimen to specimen, presumably because of a large and variable degree of internal disorder. Rhombohedral-105 boron (R-105) forms black crystals with metallic luster. There are three types of icosahedra differing in B—B bond lengths. There are also fused icosahedra in trimers and other units as large as a B84 unit in the form of a truncated icosahedron. 

Figure 10.47. Structure (j) (truncated icosahedron) is well known to the chemical community as buck-minsterfullerene, C6o, comprising hexagons and pentagons. It has been well established, both chemically and geometrically, that the pentagons in the structure are necessary to effect three-dimensional closure, and without them only open, two-dimensional graphitic layers are formed. All fullerenes, and even the topical Bucky tubes (Figure 10.2), that consist of fused hexagons are open at both ends unless pentagons are incorporated into the structure.

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