Augmentation of nets

An augmented net, which is indicated by an appendix -a to the three letter code of the basic net, is obtained from its underlying basic net by replacing all vertices with their respective coordination figure, i.e. polyhedron or polygon. For instance, all the vertices of the bcu net are replaced with cubes, and the (two different kinds of) 4-coordinated vertices of the pts net with squares and tetrahedra, respectively (see Figure below).

The first obvious advantage of such representations is that it is much easier to identify and to perceive the actual coordination environment of the vertices; not only the coordination number and type, but also their relative orientation to each other, so the local geometry of the vertices is explicitly included and visualized. In this sense it is also helpful in terms of a more intuitive or visual way of classification of nets, for instance, if we investigate all the possible nets that are assembled by a combination of certain node-types, say, tetrahedra and triangles, or trigonal prisms with squares and so on. However, augmentation is beneficial in particular in order to elucidate relationships between nets that are similar to each other: Note that the vertices of the augmented version of a given net have different coordination numbers, coordination sequences and vertex symbols; and these specifications – the topology – may be identical with another basic net that has been derived by the deconstruction of the chemical compound leading to this specific net description, for instance bcu-a is identical with the net of polycubane (pcb).

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