Crystal lattices consist of repeating units of a molecule, ion, or atom arranged in a symmetrical array. One can imagine a wallpaper pattern with a repeating design that extends in three dimensions. Similarly, the only difference between each repeating molecule in a crystal is a translation and perhaps a rot ation extended in three dimensions to comprise a beautiful, well-ordered crystalline solid with smooth edges. Crystals occur in several forms, from those we encounter daily--ice, salt, table sugar, metals--to the more precious gems--quartz and diamond--to finally the ones artificially created--protein, and even DNA.

Crystallographers describe the repeating unit of a crystal lattice, the unit cell, by the length of its edges and angles between them. This aids in classifying the 14 different kinds of lattices that are categorized into seven crystal systems: Cubic, Tetragonal, Orthorhombic, Monoclinic, Triclinic, Rhombohedral, and Hexagonal. Each of the...