This handout is taken from Dave Sherman's University of Bristol Mineralogy Page Translational Operations Suppose we have a point (x,y,z). We can translate that point by a vector (a,b,c) to get the new point (x+a, y+b, z+c). The two points (x,y,z) and (x+a,y+b,z+c) are related to each other by a translation operation. A set of points that are related to each other by translational operations is said to have translational symmetry. The internal atomic arrangement in a crystal has translational symmetry. That is, every point in a crystal is repeated by a set of translation vectors. The set of points generated by the translation vectors is called a lattice. Note that the atomic arrangements in glasses, liquids and gases do not have translational symmetry. Lattices in 2-dimensions In two-dimensions, we will have two translation vectors. There are five unique ways to set up a 2-D lattice.