Explain the elements of symmetry giving suitable examples.

The elements of symmetry are fundamental concepts in crystallography, mineralogy, and economic geology as they describe the orderly and repetitive patterns within crystals. Symmetry elements are geometric features about which a crystal structure is invariant under specific operations. The primary elements of symmetry include planes of symmetry, axes of symmetry, and centers of symmetry.

A plane of symmetry (mirror plane) is an imaginary plane that divides a crystal into two equal and symmetrical halves, such that one half is the mirror image of the other. When a crystal is reflected across this plane, it remains unchanged. For example, the mineral galena (PbS) often exhibits cubic symmetry with multiple planes of symmetry. In a cubic crystal, there are three mutually perpendicular planes of symmetry corresponding to the ________ _______ ________ _______ _______ ________ _______ _________ _______ _____ ____.
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