Nomenclature for Single Nets Schlafli and Vertex Symbols

1 Nomenclature for Single Nets Schlafli and Vertex Symbols 

The topological classification of an individual extended motif can be accomplished according to generally accepted criteria used in a variety of structural contexts that are here described. First, however, we want briefly to mention the pioneering work of the researchers who introduced the basic concepts for the rationalization, enumeration and classification of the extended crystal structures, using different approaches. 

A fundamental contribution is represented by a famous series of articles and books on crystal chemistry published many years ago by A. F. Wells [4], who analysed and classified a great number of nets. Fie emphasized the importance of describing a crystal structure in terms of its basic topology such a description not only provides a simple and elegant way of representing the structures but also evidences relations between structures that are not always apparent from the conventional descriptions. Wells introduced a method for the systematic generation of 3D arrays from 2D nets and also described many hypothetical motifs that were successively discovered within the realm of coordination polymers or of other extended systems. Flis results included a list of many simple nets described with only one kind of node (uninodal) or with two nodes of different connectivity (mainly binodal 3,4-connected). 

The studies of J. V. Smith focused on the classification of zeolites and related materials with tetrahedral nodes of the T04 type [16], He described a prolific number of frameworks that were discovered mostly by hand treatment, using systematic methods. Such methods include permutation of up-down linkages between identifiable two-dimensional layers in zeolites, as well as permutations of linkages between identifiable polyhedra. 

An empirical search by O Keeffe [17] for uninodal four-connected nets resulted in the recognition of 168 distinct types (many of which were unseen by Wells). 

---