Nets as tilings and the concept of transitivity

It would be nice with a nomenclature with a complexity in between the convolution of the vertex symbols and the simplicity of the genus. A possible approach based on nets as tilings was suggested by O. Delgado-Friedrich el al. in 1999 and elaborated by O. Delgado-Friedrich, M. O Keeffe and co-workers in subsequent years [11,14-16]. 

In short, it is based on constructing polyhedra the tilesf using the rings formed by the net, that completely fills space. There arc many ways to do this, so it was proposed that the shorte.st rings in the structure should be used as the faces of the tiles, so that for each net there would be only one natural tiling. 

We can now describe the net by this set of numbers, pgrs, called the tramitivity of the net. The point of this is that we will have a set of numbers, basically describing the complexity of the net, that again are independent of the type of connectivity at each node, and also of the sixe of the rings formed. 

It has been proposed to name different classes of 3D-nets in descending order of symmetry f 15,161 

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