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ssss1 Miller indices of various crystal faces on a cube depend on their relationship to the crystallographic axes.
ssss1 Isometric octahedron outlined in blue possesses eight faces; the form face {111} is outlined in bold blue.
Miller indices are a symbolic language that allows us to represent the spatial relationship of any crystal face, cleavage face or crystallographic plane with respect to the crystallographic axes.
4.6.6 Form indices
Every face in a form has the same general relationship to the crystallographic axes and therefore the same general Miller index, yet every face in a form has a different specific relationship to the crystallographic axes and therefore has a different Miller index. These statements can be clarified by using an example. ssss1 shows the common eight‐faced isometric form called the octahedron.
ssss1 Five common forms in the isometric system: (a) cube, (b) octahedron, (c) dodecahedron, (d) tetrahedron, (e) pyritohedron.
Many other forms exist. Every crystal form has a form index, which is the Miller index of the form face placed in brackets. Each form consists of one or (generally) more faces and each face possesses a Miller index different from that of every other face in the form. Every crystal system has a characteristic suite of forms that reflect the unique characteristics of the crystal lattice of the system, especially the relative lengths of the three crystallographic axes that directly or indirectly reflect the lengths of the unit cell edges. The forms that are characteristic of each class (space point group) in each crystal system are beyond the scope of this text (see Klein and Hurlbut 1985). However, a brief review of some common forms in each crystal system is appropriate.