Symmetry is understood a sort of regularity in the arrangement of faces on the body of a crystal. Symmetry is a property of fundamental importance for a crystal.

**Symmetry and
Crystallographic axis **

**i) ****Symmetry **

**ii) ****Crystallographic
axis **

**Symmetry:**

Symmetry is understood a sort of
regularity in the arrangement of faces on the body of a crystal. Symmetry is a
property of fundamental importance for a crystal. It can be studied with
reference to three different characters, commonly called elements of symmetry.
These are:

A plane of symmetry An axis of symmetry Centre of symmetry

**A plane of symmetry**

Any imaginary plane passing
through the centre of a crystal in such a way that it divides the crystal in
two exactly similar halves is called plane of symmetry. In other words, a plane
of symmetry is said to exist in a crystal when for each face, edge or solid
angle there is another similar face, edge or solid angle occupying identical
position on the opposite side of this plane.

**An axis
of symmetry:**

It is defined as an imaginary
line in a crystal passing through its centre in such a way that when a crystal
is given a complete rotation along this line a certain cryatl face comes to
occupy the same position at least twice. The nature of the axis of the symmetry
into one of four types:

**Axis of Binary or twofold symmetry**

This requires that a crystal must
be rotated by an angle of 180^{o} to bring the reference face occupy
the same position.

**Axis of Trigonal or threefold symmetry**

It is that axis on which a
crystal must be rotated by an angle of 120^{o} for a reference face to
occupy the same position again in space.

**Axis of tetragonal or fourfold symmetry**

It is that axis on which the
crystal must be rotated by an angle of 90^{0} to bring a reference face
in the same position in space.

**Axis of hexagonal or six fold symmetry:**

In which
a rotation of 60^{0} is required to fulfil the condition of repetition
of reference face.

**Centre of symmetry**

A crystal said to possess a
centre of symmetry if on passing an imaginary line from some definite face,
edge or corner on one side of the crystal through its centre another exactly
similar face or edge or corner is found on the other side at an equal distance
from the centre.

**ii) CRYSTALLOGRAPHIC AXES**

These are also termed as axes of
reference and are simply certain imaginary lines arbitrarily selected in such a
way that all of them pass though centre of an ideal crystal. The concept of
axes of reference is based on the fact that exact mathematical relations exist
between all the faces on a given crystal with reference to its centre.

In crystallography following
general assumptions have been universally agreed upon regarding these
crystallographic lines:

a) Three
Straight Lines, essentially passing though a common centre and varying in
mutual relationships with respect to their lengths and angular inclinations
from: all equal, Interchangable and it right to all unequal and inclined with
each other.

b) Four
straight lines, essentially passing through a common centre; one vertical,
being unequal to the other three but at right angles to them. The three
horizontal axes are separated

from each
other at 120^{0}

The concept of crystallographic axis has been the basis of
classifying all, the crystalline substances into six crystal systems.

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