Iglesias Juan E
Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas, Cantoblanco, 28049 Madrid, Spain.
Acta Crystallogr A. 2006 May;62(Pt 3):195-200. doi: 10.1107/S0108767306008798. Epub 2006 Apr 14.
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.
分析了具有重复周期P的等径球紧密堆积的空间群对称性与其表示的Zhdanov符号的对称性质之间的关系。当假设堆积具有某种对称性时，证明是直接明了的，并研究了这种对称性如何在Zhdanov符号的结构中体现。这些证明大多在文献中有记载，严谨程度各不相同。然而，当反过来进行推导时，即假设Zhdanov符号具有某些对称性质，并研究其对它所表示的多型结构对称性的相应影响时，证明就会稍微复杂一些，这也许可以解释为什么这些证明被回避或被视为“显而易见”而不予理会。
