In such symbols, signifying the symmetry, the numbers indicate axes of rotational symmetry. For example "3" symbolizes a threefold-rotational axis, which means that the crystal is mapped onto itself every 120 degrees of rotation around this axis. A fourfold-rotational axis (4) means that the crystal, being rotated around this axis, is mapped onto itself every 90 degrees of rotation.
A number-with-an-*-added, for instance 4*, means that the crystal has one or more roto-inversion axes, and such a roto-inversion axis means that if we first rotate the crystal with an amound that is implied by the number, and then invert the crystal, it will be mapped onto itself. To "invert" is also a symmetry-operation, here it means that (directly after the rotation) each part of the crystal is interchanged with its corresponding part that is diagonally situated at the other end of the crystal, i.e. those parts (all parts) are being mirrored (reflected) across one point, and that point is located in the geometrical center of the crystal.
In the literature the possession of a roto-inversion axis is indicated with a horizontal dash above the number.
The presence of a plane-of-symmetry (= a mirror plane) is indicated with the symbol m. In this way 2/m for example means that the crystal has a two-fold rotation axis with a miror plane perpendicular to it.
2/m 2/m 2/m means that the crystal possesses three twofold rotational axes (perpendicular to each other), having a miror plane perpendicular to each axis.
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