Elements of Symmetry of a Crystal

Updated: May 2, 2020

Elements of Symmetry:

There are three main elements of symmetry. Those are

1) Axes of Symmetry 2) Plane of Symmetry 3) Center of Symmetry

Axes of symmetry:

If the crystal repeats identical/symmetrical positions during its rotation through 360°, then the symmetry is known as axis of rotation.

In the case of a simple cubic structure, four identical positions in one complete rotation possible along the axis when it pass through the mid points of two opposite faces. Therefore, the crystal has four fold axis of symmetry for each 90° (360°/n=4) rotation.

Plane of Symmetry:

The planes which cut a crystal into two halves so that each half is a mirror image of the other half i.e the plane divides the crystal into identical pieces then the plane is known as plane of symmetry.

There are three planes can easily be constructed, each parallel to opposite faces of the cube, six planes diagonally of the cube which are passing through opposite sides of the cube.

There fore for a simple cubic structure, there are ‘9’ planes of symmetry.

Center of symmetry:

This refers to a point in the crystal such that a line drawn from any lattice point in the crystal through this point gives equal distance. The cubic has only one such center of symmetry.

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