GEOL 2540 Lecture Notes - Lecture 4: Icosahedron, Auguste Bravais, Trapezohedron

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Symmetry with respect to: (1) a point (1) a point i = center of symmetry. Threefold (diad) (triad) (3) symmetry with respect to a plane mirror plane m. Symme try ope ra tions: (1) inversion (2) rotation (3) (3) reflection ti fl. Combine rotation about an axis with inversion through a point on that axis. Two-fold inversion axis is equivalent to a symmetry plane perpendicular to that axis m. 4 i(= 1), m(= 2), 3, 4, 6, 1, 2, 3, 4 and 6. Is the number of combinations of symmetry elements infinite? elements infinite? i m. There are only 32 non-identical combinations of symmetry elements that are compatible with each other and pass through a common point each other and pass through a common point. Crystals whose symmetry is described by one of the 32 p. g. belong to the same crystal class 32 crystal classes f p. g. g m y. 3m 32 3m 3 3 m3m 432 43m m3 23.

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