Taxonomy of periodic nets and the design of materials

The concept of a natural tiling for a periodic net is introduced and used to derive a transitivity associated with the structure. It is accordingly shown that the transitivity provides a useful method of classifying polyhedra and nets. For design of materials to serve as targets for synthesis, structures with one kind of edge (edge transitive) are particularly important. Edge-transitive polyhedra, layers and 3-periodic nets are then described. Some other nets of special importance in crystal chemistry are also identified.