Nets with polyhedral cavities

In certain 3D nets there are well-defined polyhedral cavities, and the links of the net may alternatively be described as the edges of a space-filling assembly of polyhedra. At least four links must meet at every point of such a net, and the most important nets of this kind are, in fact, 4-connected nets. Space-filling arrangements of polyhedra leading to such nets are therefore described after we have dealt with the simpler 4-connected nets. 

We have supposed that in any system all the points together form one connected net, that is, it is possible to travel along links from any point to any other. There are some very interesting structures in which this is not possible, namely, those consisting of two or more interpenetrating (interlocking) structures (Fig. 3.17). 

We shall now give examples of molecular and crystal structures based on 2-, 3-, and 4-connected systems. Although logically the cyclic and chain systems (corresponding to p = 2) should precede the polyhedral ones (p 3) we shall deal with the latter first so that we proceed from finite to infinite groups of atoms. This kind of treatment cuts right across the chemical classification of molecules and 80 

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