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Attempt at showing the convential cubic F lattice in blue, and moving from (0 0 4) to (-2 -2 2) to see the ABC stacking with hexagonal lattice vectors in green. The thin cylinder connects atoms in adjacent ABC layers. In a twin, so ...ABCABCABC... becomes ...ABCABACBA..., that thin cylinder would change direction at the B interface. The B layer is the unchanged interface. Note that "ABA" at the interface looks like hexagonal close packing. There is one 2x2 array of cubic F cells drawn.
Patrick Welche, Inference Group, Cavendish Laboratory.