Earth Materials. John O'Brien

the indices of a single face, called the form face, are chosen and placed in brackets to indicate that they refer to the form indices. The rule for choosing the form face is generally to select the top face if there is one, or the top right face if there is one, or the top right front face if there is one. In the case of the octahedron, the top right front face is the face that intersects the positive ends of the a₁‐axis (front), the a₂‐axis (right), and the a₃‐axis (top) and has the Miller indices (111). The form indices for all octahedral crystals are the Miller indices of the form face placed between curly brackets {111}. Similarly the form indices for the cube (see Figure 4.22), in which the faces intersect one axis and are parallel to the other two are {001}, the Miller indices of the top face, whereas the form indices for the dodecahedron, in which each face intersects two axes at unity and is parallel to the third is {011}, the indices for the top, right face.

Figure 4.24 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.

      4.6.7 Common crystal forms in each system

       Isometric (cubic) system forms

All forms in the isometric system are closed forms. Common crystal forms in the isometric system include the cube, octahedron, dodecahedron, tetrahedron, and pyritohedron (Figure 4.24). These forms may occur alone or in combination with each other. Common isometric minerals, their crystal forms, and form indices are summarized in Table 4.6.

These form indices are also used to describe cleavage in isometric minerals. These minerals include halite and galena, which possess cubic cleavage {001} with three orientations of cleavage at right angles; fluorite, which possesses octahedral cleavage {111} with four cleavage orientations; and sphalerite, which possesses dodecahedral cleavage {011} with six orientations of cleavage.

Table 4.6 Common isometric crystal forms, form indices, form descriptions, and minerals.

Crystal form	Form indices	Form description	Minerals that commonly exhibit crystal form
Cube	{001}	Six square faces	Halite, galena, pyrite, fluorite, cuprite, perovskite, analcite
Octahedron	{111}	Eight triangular faces	Spinel, magnetite, chromite, cuprite, galena, diamond, gold, perovskite
Dodecahedron	{011}	12 diamond‐shaped faces	Garnet, sphalerite, sodalite, cuprite
Tetrahedron		Four triangular faces	Tetrahedrite, sphalerite
Pyritohedron	{h0l}	12 pentagonal faces	Pyrite

Figure 4.25 Common crystal forms in the tetragonal crystal system: (a) tetragonal prism in combination with a pinacoid, (b) tetragonal dipyramid, (c) tetragonal dipyramid in combination with a tetragonal prism.

Table 4.7 Common tetragonal crystal forms, form indices, form descriptions, and minerals.

Crystal forms	Form indices	Form description	Minerals that commonly exhibit crystal form
Tetragonal dipyramid	{111} {hh1} {011} {0kl} and variations	Eight triangular faces; top four separated from bottom four by mirror plane	Zircon, rutile, cassiterite, scheelite, wulfenite, vesuvianite, scapolite
Tetragonal prism	{010} {110} and variations	Four rectangular faces parallel to c‐axis	Zircon, scheelite, vesuvianite, rutile, malachite, azurite, cassiterite, scapolite
Tetragonal disphenoid	{0kl}	Four triangular faces; alternating pairs symmetrical about c‐axis	Chalcopyrite
Basal pinacoid	{001}	Pair of faces perpendicular to c‐axis	Vesuvianite, wulfenite

       Tetragonal system forms

Tetragonal crystals can possess closed and/or open forms. Common closed crystal forms in the tetragonal crystal system include different eight‐sided dipyramids. Common open forms include four‐sided and eight‐sided prisms and pyramids, as well as pinacoids and pedions. Typical crystal forms and associated minerals in the tetragonal crystal system are shown in Figure 4.25 and Table 4.7.

       Hexagonal system (hexagonal division) forms

Common crystal forms in the hexagonal system include 6–12‐sided prisms, dipyramids, and pyramids. Pinacoids and pedions are also common. Some selected examples of common crystal forms and minerals in the hexagonal system are illustrated in Figure