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The optical gyrations of a domain-free section and of a twinned section of the nonlinear optical crystal KTiOPO4 have been measured using a high-accuracy universal polarimeter. An optical gyration at 6328 Å equivalent to an optical rotation of +22° mm-1 together with a significant circular dichroic contribution was found in the domain-free ({\bar 2}10) section whereas equivalent rotations varying between +14 and -20° mm-1 were found in different regions of the twinned section. The absolute indices of the faces of the samples and the existence of twinning in the second section have been established using X-ray anomalous scattering. The regions of opposite optical chirality in the twinned sample have been shown to correlate with those of opposite structural chirality. The results are used to show that the twinning operation in this KTiOPO4 crystal must be one of the twofold rotations 2[010] or 2[100].

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