Polyhedral molecular geometries

In the Preface to the Third Edition of his Regular Polytopes [20], the great geometer H. S. M. Coxeter calls attention to the icosahe-dral structure of a boron compound in which twelve boron atoms are arranged like the vertices of an icosahedron. It had been widely believed that there would be no inanimate occurrence of an icosahedron, or of a regular dodecahedron either. 

In 1982, the synthesis and properties of a new polycyclic C2oH2o hydrocarbon, dodecahedrane, was reported [21], The twenty carbon atoms of this molecule are arranged like the vertices of a regular dodecahedron. When, in the early 1960s, H. P. Schultz discussed the topology of the polyhedrane and prismane molecules (vide infra) [22], at that time it was in terms of a geometrical diversion rather than true-life chemistry. Since then it has become real chemistry. 

It should be reemphasized that the above high-symmetry examples refer to isolated molecules and not to crystal structures. Crystallography has, of course, been one of the main domains where the importance of polyhedra has been long recognized, but they are not less important in the world of molecules. 

In the First Edition of Regular Polytopes, Coxeter stated, ... the chief reason for studying regular polyhedra is still the same as in the times of the Pythagoreans, namely, that their symmetrical shapes appeal to one s artistic sense [23], The success of modem molecular chemistry does not diminish the validity of this statement. On the contrary. There is no doubt that aesthetic appeal has much contributed to the rapid development of what could be termed polyhedral chemistry. One of the pioneers in the area of polyhedral borane chemistry, Earl Muetterties, movingly described his attraction to the chemistry of boron hydrides, comparing it to M. C. Escher s devotion to periodic drawings [24], Muetterties words are quoted here [25]  

When I retrace my early attraction to boron hydride chemistry, Escher s poetic introspections strike a familiar note. As a student intrigued by early descriptions of the extraordinary hydrides, I had not the prescience to see the future synthesis developments nor did I have then a scientific 

The polyhedral description of molecular geometries is, of course, generally applicable as these geometries are spatial constructions. To emphasize that even planar or linear molecules are also included, the term polytopal could be used rather than polyhedral. The real utility of the polyhedral description is for molecules possessing a certain amount of symmetry. Because of this and also because of the introductory character of our discussion, only molecules with relatively high symmetries will be mentioned. 

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The discovery of buckminsterfullerene (see, also, in Chapter 1) with its intriguing shape, focused attention to polyhedral molecular geometries even by many outside of chemistry. The event is often considered to be the birth of nanoscience and nanotechnology although they existed before even though under less fancy names. Buckminsterfullerene, C6o, discovered in 1985 [30], was the first runner-up for the title, Molecule of the Year in 1990 [31], and received the title in 1991 [32], On this occasion, the Editorial of Science stated, among others, that... 

Polyhedral molecular geometries have made even the mass media recently with the discovery of buckminsterfullerene [3-17], (Figure 3-25), and especially with the whole new chemistry of the fullerenes (see, e.g., Ref [3-18]). Buckminsterfullerene was named Molecule of the Year in the December 20,1991, issue of Science magazine [3-19] while it was only the first runner-up the previous year [3-20]. Although even a runner-up status is of the highest prestige, in 1990 even the structural formula was drawn erroneously (cf Ref [3-21]), and buckminsterfullerene was referred to as a distant cousin of diamond [3-20]. By December, 1991, all this had changed, and the Science editorial [3-22] stated. 

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