However we write 4 / m, not 4 / m, because both 4 and 4 generate four points. Analogously, in the case when both 3 and 3 axes are present, 3 should be written. Since 6 generates 6 points, and 3 generates only 3, 6 should be written instead of 3 / m (not 6 / m, because 6 already contains the mirror plane m). For example, the 3 / m combination is equivalent to 6. If a rotation and a rotoinversion axis generate the same number of points, the rotation axis should be chosen. For example, rotation axes 3, 4, 5, 6, 7, 8 generate 3-, 4-, 5-, 6-, 7-, 8-point patterns, respectively. Higher symmetry means that the axis generates a pattern with more points. If two or more axes have the same direction, the axis with higher symmetry is shown. the plane is perpendicular to axis n), then they are denoted as a fraction n / m or n / m.
If a rotation axis n and a mirror plane m have the same direction (i.e. The direction of a symmetry element corresponds to its position in the Hermann–Mauguin symbol. Hermann–Mauguin symbols show non-equivalent axes and planes in a symmetrical fashion. The direction of the mirror plane is defined as the direction of the perpendicular to it (the direction of the 2 axis). 2 is equivalent to a mirror plane and usually notated as m. The rotoinversion axes are represented by the corresponding number with a macron, n - 1, 2, 3, 4, 5, 6, 7, 8. For improper rotations, Hermann–Mauguin symbols show rotoinversion axes, unlike Schoenflies and Shubnikov notations, that shows rotation-reflection axes. Rotation axes are denoted by a number n - 1, 2, 3, 4, 5, 6, 7, 8. 1.3 Groups with several higher-order axes.1.1 Groups without higher-order axes (axes of order three or more).
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