Crystal Symmetry is the ability of a crystal to shape by nature and has a symmetrical shape. It's also referred about the occupation of diamond cutters.
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Isometric
Corundum crystals belong to the ditrigonal-scalenohedral class of the trigonal symmetry D63d - R 3-C(L33L23PC) with symmetry elements: • Mirror-turn axis of the sixth order (ternary inversion axis) • Three axes of the second order normal to it • Three symmetry planes normal to the axes of the second order and intercrossing along the axis of the highest order • Symmetry center
Reflection symmetry, reflectional symmetry, line symmetry, mirror symmetry, mirror-image symmetry, or bilateral symmetry is symmetry with respect to reflection
line symmetry, rotational symmetry, mirror symmetry &liner symmetry
Asymmetry, Radial Symmetry, and Bilateral symmetry.