Symmetry operations are one after which the crystal lattice remains invariant. There are four basic symmetry operations- Translation, Rotation, Reflection and Inversion. Combining two or more basic symmetry operations, we have further three operations- Rotation-inversion. Screw and Glide. The concept of translation and rotation symmetry, you will find here. The crystal has two, three, four and six-fold rotational symmetry axes, not the five, seven, eight-fold etc. rotational symmetry. This fact has been explained in detail.
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