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Figure 1
Reference-frame manipulations required before an input structure can be evaluated for fit into a higher-symmetry target space group. All the vertical arrows (except for the one labeled `translation x') represent change of basis operators consisting of a rotation matrix and a translation vector, each containing rational values (ratios of small whole numbers). The operators can be composed together to form an overall operator (RT), for example, transforming the input structure into a setting that is consistent with the reference frame of the candidate symmetry. An additional real-valued translation x optimizes the position of the input model with respect to the symmetry axes of the target space group. The reference frames used for evaluating equations (1)–(3)[link][link][link] are indicated. Importantly, the final `conventional setting' structure is still exactly superimposable with the input structure. The imposition of target symmetry constraints is a separate operation (horizontal arrow) and is discussed in §[link]2.6.

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ISSN: 2059-7983
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