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How to Identify Authentic Waterford Crystal Marks

Crystal metrics: The equilibrium shape of a crystal is dictated by the energy of its low-index crystal facets, and so one can often identify facet types just by looking at the symmetry of the crystal and the relative angles between planes. For a hexagonal crystal with a ratio of lattice parameters c/a = 1.65, compute the angles between each pair of the following set of planes: the (1012), (2112), and (0001) planes. (9 points) (Yifi Fn)