To discuss the seven crystal systems in detail, we have to establish some understanding of crystal geometry. The notation used to describe crystals is known as “Miller indices”. Before William H. Miller (1801-1880) devised this mathematical system for describing any crystal face or group of similar faces (forms), there was a considerable amount of confusion due to the many different descriptive systems. Miller applied relatively simple mathematics to the problem, and his notation has become the universal language for all crystallography.

The Miller indices of a cubic structure are shown below, and it can be seen that the planes are described by three whole numbers, fractions are not allowed. To determine the Miller indices of a plane, we first determine where the plane crosses each intercept. We take the reciprocal of each, and convert them to whole numbers. Negative indices are described by a bar on top of the integer, and planes are described as three integers surrounded by round brackets. Families of planes, for example, (100) (001) and (010) can be described collectively by using a different type of bracket {100}.