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Figure 2
Tree-diagram that shows the increase in the number of variants for the first two generations. Degeneracy is not taken into account. The operators that produced the variants are also indicated. Starting from the progenitor, one can trace each particular variant by following a path determined by the operators used to create it. Note that the numerical values of matrices corresponding to H1–6 symmetry operations are known, since they operate on the Pr, whereas those corresponding to [{\bi C}_{\bi 1 - 12}^*] are not known, since they operate on crystals of different orientations. To indicate this, the latter are denoted with an asterisk superscript. Therefore, symmetry operation [{\bi C}_{\bi 12}^*] operating on, for example, A3 is not represented by the same matrix as [{\bi C}_{\bi 12}^*] operating on A4. As shown below, finding the numerical values of these matrices is not necessary.

ISSN: 2052-5206
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