What Is a Fullerene

The conventional definition, and the one to be used in the present chapter, is that a fullerene C is a carbon cage where the atoms define the vertices of a divalent polyhedron with 12 pentagonal and ti/2- 10 hexagonal faces. Fullerene polyhedra of this type are realizable for = 20 and for all even n 24, i.e., n = 20 + 2k(k 1) where k counts the hexagonal faces. All experimentally characterized fullerenes comply with this definition, and in fact all so far found have in addition isolated pentagons isolated-pentagon fullerenes are possible for = 60 and for all even n 70. 

Almost any divalent polyhedron, spherical, toroidal, or of higher genus, is at least conceivably a candidate for an sp carbon framework if reasonable bond lengths and angles can be achieved, and so there has naturally been some discussion in the literature of extended definitions of fullerenes (e.g.. Refs. 8-17). Exotic topologies are dealt with elsewhere in the present volume in the chapters by Kirby and Klein, but even within the class of pseudospherical polyhedra other face sizes are possible. The Euler formula for an n-vertex divalent spherical polyhedron is 

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In order to see the question in context, it will be necessary to address a number of problems in fullerene systematics, namely What is a fullerene How many structures are hypothetically possible, and how may they be constructed What spectra are to be expected of fullerenes What is the connection between jt-electronic properties and overall stability The present chapter deals with some of these questions in relation to the central problem of geometric and electronic structure. A more detailed account that includes discussion of isomerization, growth, and formation may be found elsewhere. ... 

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