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ssss1 Representative crystal faces that cut one, two or three crystallographic axes. See text for further discussion of parts (a–f).

Of course, some sets of planes or their projections intersect the positive ends of crystallographic axes (ssss1b, c, and e). Others, with different spatial orientations with respect to the axes, intersect the negative ends of crystallographic axes (ssss1a). Still others, with yet different orientations, intersect the positive ends of one or more axes and the negative ends of other crystallographic axes (ssss1d, f). Given the myriad possibilities, a simple language is needed that allows one to visualize and communicate to others the relationship and orientation of any set of crystal planes to the crystallographic axes. The language for identifying and describing crystallographic planes involves the use of symbols called Miller indices, which has been employed since the 1830s and is explained in the following sections.

In any crystal, the three crystallographic axes have a characteristic axial ratio, typically grounded in the cell edge lengths of the unit cell. No matter how large the mineral becomes during growth, even if it experiences preferred growth in a particular direction or inhibited growth in another, the axial ratio remains constant and corresponds to the axial ratio implied by the properties of the unit cell.