Zhdanov's rules work both ways.
The relationship between the space-group symmetry of a close packing of equal balls of repeat period P and the symmetry properties of its representing Zhdanov symbol is analyzed. Proofs are straightforward when some symmetry is assumed for the stacking, and it is investigated how this symmetry is reflected in the structure of the Zhdanov symbol. Most of these proofs are documented in the literature, with variable degrees of rigor. However, the proof is somewhat more involved when working backwards, i.e. when some symmetry properties for the Zhdanov symbol are assumed and the corresponding effect on the symmetry of the polytype structure it represents is investigated, which may explain why these proofs are avoided or shrugged off as ;easily seen', 'obvious' and the like.
Iglesias
Juan E
JE
Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, Cantoblanco, 28049 Madrid, Spain. jeiglesias@icmm.csic.es