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Figure 4
Resolving indexing ambiguities in the diffraction pattern from Fig. 1[link](b) using a maximum clique. (a) Calculation of d1, the observed distance in reciprocal space between two reflections. A reference reflection A and a candidate reflection B are projected back on to the Ewald sphere from their positions on the detector. Inset: the distance between the reflections A and B is measured in reciprocal space. (b) Calculation of d2, the predicted distance in reciprocal space. Given the reference reflection A and its candidate index (1, 0, 1), there are four possible symmetry operators applicable to reflection B and its candidate index (4, 1, 1). Two of them are not correct, as the predicted distances d2 do not match the observed distance d1. (c) Complete graph from Fig. 1[link](b). Each node represents a single reflection paired with a candidate Miller index and one of four symmetry operators of the reciprocal-lattice point group. The boxes are labeled first with an arbitrary identification of the spot (a spot ID) and then with the Miller index being examined. For example, the central spot is spot number 4, with index (−4, 0, −2). The nodes are colored by degree (number of connections), with green representing many connections and red representing one. Edges represent spot connections (see text). (d) Plotting the eight reflections from the correct maximum clique in (c) in reciprocal space. The plotted reflections form a right-handed basis and intersect the Ewald sphere.

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