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The number of different isomers and derivatives is often mentioned in undergraduate chemistry courses, in order to rationalize the vast variety of existing (and new, unsynthesized) compounds. The mathematical techniques used for enumeration are not, however, described in any detail. The link between symmetry and the number of isomers (derivatives) is thus left unexplored in the lectures, ostensibly due to the complex mathematics and unfamiliar concepts of permutation groups. Furthermore, isomer enumeration usually appears in the discussion of classes of organic compounds where it is used to deduce the number of chiral molecules. Inorganic-compound enumeration is virtually untouched by the undergraduate textbooks or lectures. We wish to demonstrate that the powerful Polya enumeration method (1) can be used profitably with the widely available PC software, such as Mathematica (2). Chemical enumeration is described in various special textbooks on graph theory, but even there it has not been applied to the examples of well-known organic and especially inorganic molecules. The examples discussed in such textbooks are predominantly alkanes and polycyclic aromatic hydrocarbons. We shall demonstrate that even simple inorganic compounds (with geometries of regular polygons or polyhedra) possess a rich variety of isomers and derivatives, which can be readily enumerated by students. Furthermore, on the basis of worked examples, we show how the number of chiral organic and inorganic compounds may be deduced and used to supplement conventional discussions on group theory and symmetry in chemistry
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