Deformation twin - Twin Variants

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To identify the activated twin variant in deformation twinning, one must analyze the orientation matrices of both the matrix and the twin relative to the sample frame. In hexagonal close-packed (HCP) metals, such as those with {10-12} tensile twins, there are six possible twin variants. In body-centered cubic (BCC) metals, the {112}<111> twins exhibit twelve distinct variants. The discussion emphasizes the importance of understanding the crystallographic relationships to determine which twin variant is activated during deformation. Accurate identification of twin variants is crucial for predicting material behavior under stress.
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Given orientation matrices for matrix and twin w.r.t sample frame, how to identify the twin variant activated? For example,
in HCP metals {10-12} tensile twins have 6 variants. In BCC metals, {112}<111> twins have 12 variants.

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