Armed with the above and with our approximate knowledge of ...
Description: Armed with the above and with our approximate knowledge of the opening angle of 120°+-3°, seen here looking down onto the V almost parallel to the hinge line (FOV 14.5x15.3mm), we can finally put forth a plausible hypothesis: Unless the indices are improbably large, the one possibility for the twinning plane is (1 2 -1), which would result in a calculated angle of almost exactly 59° against (100), and thus in an opening angle between the (100) faces of the two wings of almost exactly 118°. (I've spent a while staring at the crystal models on the webmineral page for Kyanite, trying to see how to cut up the lattice and reattach it to a mirror image of itself along various possible planes. It doesn't look too convincing to me. But perhaps the real, lattice-level twinning operation is a glide reflection rather than a reflection.)