The Miller indices are referenced to the crystallographic axes of a crystal. They therefore do not have to be oriented at right angles (and are not for monoclinic and triclinic crystals). For orthorhombic crystals, there is unfortunately no convention on how to define the a axis.

The Miller indices are found by determining the points at which a given crystal plane intersects the three axes, say at ,,and If the plane is parallel an axis, it is given an intersection The Miller index for the face is then specified by ([img]
scienceworld.wolfram.com/chemistry/mimg30.gif[/img],[img]
scienceworld.wolfram.com/chemistry/mimg31.gif[/img],[img]
scienceworld.wolfram.com/chemistry/mimg32.gif[/img])where the three numbers are expressed as the smallest integers, and negative quantities are indicated with an overbar. A face, when given with the crystal class, determines a set of faces known as a form and is denoted The vector normal to a face is specified as