Question

How many types of three dimensional lattices are present in crystals?

Answer 1

Hint: The Bravais lattice definition of an infinite array of discrete points is generalised in crystallography by using the concept of a unit cell, which contains both the space between the discrete lattice points and any atoms in that space. Unit cells are divided into two categories: primitive unit cells and non-primitive unit cells.

Complete answer:
The Bravais lattice definition of an infinite array of discrete points is generalised in crystallography by using the concept of a unit cell, which contains both the space between the discrete lattice points and any atoms in that space. Unit cells are divided into two categories: primitive unit cells and non-primitive unit cells.
As repeated once for each distinct lattice point, the unit cell, whether primitive or not, must precisely fill the whole space with no overlap or gaps.
There are 14 Bravais lattices in three-dimensional space. One of the seven lattice systems is combined with one of the centering forms to produce these. The following are the centering forms that define the positions of the lattice points in the unit cell:
Primitive (P): only the cell corners have lattice points (sometimes called simple)
Base-centered (A, B, or C): lattice points on cell corners, plus one additional point in the middle of each face of one pair of parallel cell faces (sometimes called end-centered)
Body-centered (I): lattice points on cell corners, plus one more point in the cell's middle
Face-centered (F): lattice points on cell corners, plus one extra point in the middle of each of the cell's faces
Triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic lattice systems are among the 14 Bravais lattices. A lattice system is assigned to a collection of point groups and their corresponding space groups in a crystal system.
Bravais lattices are made up of unit cells with internal symmetry. Since there aren't many ways to have internal symmetry, there are just 14 Bravais lattices instead of the seven crystal structures.

Note:
Triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic lattice systems are among the 14 Bravais lattices. A lattice system is assigned to a collection of point groups and their corresponding space groups in a crystal system.
Bravais lattices are made up of unit cells with internal symmetry. Since there aren't many ways to have internal symmetry, there are just 14 Bravais lattices instead of the seven crystal structures.