In the geometric sense, a figure is symmetrical if, when moved, it looks as if it has not been moved. The different kinds of symmetry are defined by the way an object may be moved and yet seem to remain the same. Reflection, or bilateral, symmetry is probably the most familiar type. A body has reflection symmetry through a plane if for every point on one side of the plane there is an identical point at the corresponding location on the other side. In other words, if half the object is a mirror image of the other half, the object has bilateral symmetry.
Translation symmetry is the basic symmetry of crystal structures.
An object possesses translation symmetry if it can be moved a certain distance in a straight line and appear to be unchanged. Such an object has a regular repeating pattern. A single figure cannot possess translation symmetry. But regular repeating patterns such as a brick wall, a tiled floor, and a crystal lattice do possess translation symmetry. Lattices can possess other symmetries as well, but they must have translation symmetry to be lattices.