ERSC 2P21 Lecture Notes - Lecture 13: Improper Rotation, Angle Of Rotation, Nicolas Steno
19 Dec 2018
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Document Summary
When a line can be passed from a point on its surface through the center and the same point is found on the line at an equal distance beyond it. Rotate through a (rotation angle) then invert around center. 3 = 3-fold rotoinversion axis (3-fold rotation axis + centre of symmetry) 4 = 4-fold rotoinversion axis: unique (can"t be resolved into combinations) 6 = 6-fold rotoinversion axis (3-fold rotation + mirror plane perpendicular) Motifs generated by rotoinversion are repeated in both the same and opposite orientation. Combinations of point symmetry: 32 combinations of the 4 point symmetry elements, 32 crystal classes = 32 point groups. Rotation axis with a perpendicular mirror plane m m. Only 32 possible combinations -- 32 crystal classes. 32 crystal classes can be divided into six crystal systems (+ one subsystem) point point. = group no symm ) centre of symm ) 32 crystal classes, six crystal systems, minimum symmetry, point group notation.
