From chemical topology to 3D geometry

The first part presents a survey of how ideas originating in chemical topology can be applied for stereochemistry; diastereoisomerism can be more easily encoded in matrix form than enantiomerism. Chirality in two or three dimensions is examined, and the simplest elements of chirality (''protochirons'') are described. Their assembly into chiral or achiral geometries with chemical relevance, including regular and semiregular polyhedra, is described. Examples of topological stereoisomerism are discussed. The second part is a bibliography including a particularization of Euler's famous formula for three-dimensional polyhedra, including cage compounds, which takes into account the possible presence of vertices of degrees two and/or four; chemical applications of this special formula are various cage hydrocarbons, fullerenes, fullerocoronands with oxygen heteroatoms, and nanotubes with oxygen or nitrogen heteroatoms which may form complexes with metallic cations; the heteroatoms serve to remedy dangling bonds at the ends of nanotubes.