The document discusses symmetry in geometry and crystallography. There are three elements of crystallographic symmetry: axis of symmetry, where a crystal can be rotated around an imaginary line to fill the same space multiple times; plane of symmetry, where an imaginary plane divides a crystal into mirror image halves; and center of symmetry, where points on the crystal are equidistant from the center along an imaginary line. Symmetry is a balanced similarity found in two halves of an object, and it is a fundamental property of the orderly arrangements of atoms in crystalline solids.

2. INTRODUCTION
Symmetry:
In geometry, symmetry is defined as a balanced and proportionate similarity that
is found in two halves of an object.

3. Crystallographic Symmetry:
In crystallography, fundamental property of the orderly arrangements of atoms
found in crystalline solids. Each arrangement of atoms has a certain number of
elements of symmetry

4. Elements of Symmetry:
There are three elements of crystallographic symmetry;
1. Axis of Symmetry
2. Plane of Symmetry
3. Centre of Symmetry

5. Axis of Symmetry:
When an imaginary line can be passed through a crystal such that
the crystal can be rotated 360o about the line to fill the same space two, three,
four, or six times,

6. Plane of Symmetry:
It is an imaginary plane which passes through the centre of a crystal can divides
it into two equal portions which are exactly the mirror images of each other.

7. Centre of Symmetry:
A centre of symmetry exists in a crystal if an imaginary line can be extended
from any point on its surface through its centre and a similar point is present
along the line equidistant from the centre.

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