By definition, crystals are periodic in three dimensions and the X-ray diffraction experiment must be understood in the context of the crystal lattice and the space group.  A lattice is a regular infinite arrangement of points in which every point has the same environment as any other point.
A lattice in 2 dimensions is called a net and a regular stacking of nets gives us a 3-dimensional lattice.
2-D net Stacks of 2-D nets
produce 3-D lattices.
Since lattices consist of infinitely repeating patterns, one needs only to look at a the smallest repeat unit to describe the lattice.  The smallest repeat unit that will generate the entire lattice (by translation) is called the Unit Cell.  It is defined by three repeat distances (a, b, and c) and three angles (α, β, γ), where αis the angle between b and c, βis the angle between a and c, and γis the angle between a and b.
Unit cell parameters(a, b, c, α, β, γ) are chosen to best represent the highest-possible symmetry of the crystal and are given right-handed axes (a is along x, b is along y and c is along z) with angles that are either all ≥90ºor all ≤90º.
There are seven different classes of unit cells that, each defined by different limiting conditions on the
unit cell parameters (a , b , c , α, β, γ).  The most general system is called “Triclinic”in which none of the
distances and angles are restricted to have any particular value.  Please note that the symbol “≠”means “is not necessarily equal to”i.e. they
might have the same value but it is not a requirement of the crystal system.
Triclinic
centeringa ≠
b ≠
c , α≠β≠
γMonoclinic a ≠b ≠c , α= γ= 90º≠β
(by convention b is the unique axis)
Orthorhombic
a≠b≠c, α= β= γ= 90º
Tetragonal
a= b≠c, α= β= γ= 90º(by definition c is the unique axis)
As more of the angles and distances are restricted, the box becomes more symmetric.
Hexagonal or Trigonal
a =
b ≠
c , α= β= 90ºγ= 120º(by definition c is the unique axis)
Rhombohedral a = b = c , α= β= γ≠90ºNote that for the hexagonal or trigonal systems, three unit cells are
necessary to see the symmetry of the system.  The choice of trigonal or hexagonal is dependent on the contents of the cell (more on this
later).
Cubic
a =
b =
c , α= β= γ
= 90ºThe most symmetric boxes are cubic and have only one variable parameter.

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