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10.5.1: Forms and Point Groups

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    On the basis of the relative positions of crystal faces and possible symmetries, crystallographers have distinguished 48 distinctly different forms. Figure 10.47, below, shows 28 examples. Symmetry is listed for each, but many of the forms can occur in crystals of more than one point group because they can be both general forms and special forms. For example, a tetragonal pyramid is the general form for crystals with symmetry 4. It is a special form for crystals with symmetry 4mm. A rhombohedron is the general form for point group 3, but is a special form in point groups 32 and 3. And, cube faces may be present in crystals with symmetry of any of the cubic point groups (23, 432, 2/m3, 43m, or 4/m32/m). The table below Figure 10.47 lists the possible forms in each of the 32 point groups.

    We should emphasize that although only 48 possible forms exist, they can have an infinite number of sizes and shapes. A disphenoid, a form consisting of four faces, may be tall and skinny or short and wide. Nevertheless, it is still a disphenoid. And Figures 10.36 and 10.37 show a crystal that contains two different pinacoids with different shaped faces.

    Forms retain their names, even if truncated by other forms. Consider the complex crystal in Figure 10.35. It contains four forms: cube, octahedron, trapezohedron, and dodecahedron. The faces corresponding to the forms do not have the same shape as they would if they were the only form in the crystal. And, in many other figures (e.g., Figures 10.28, 10.32, 10.38), pyramids and prisms truncate each other.

    Figure 10.47: 28 of the possible 48 forms

    Possible Forms in Different Point Groups

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    Most mineral crystals contain more than one form, leading to a large but limited number of possible combinations. The number of possible combinations is limited because the shape and symmetry of crystal faces depend on a crystal’s point group which, in turn depends on the atomic arrangement within the crystal. For example, if the atoms within a crystal are not arranged in hexagonal patterns, forms may not have hexagonal symmetry. Similarly, a crystal may not develop a cubic form unless atoms are in a cubic arrangement. Thus, certain forms never coexist in crystals, while others are often found together. Because the forms present in particular crystals depend on atomic arrangements, they are generally consistent for a given mineral. Uncertainty arises, however, because some minerals can have crystals with several different combinations of forms, and it is not always clear why one develops instead of another. However, if we know the point group of a crystal, we can look in the table above to see which forms may be present.

    This page titled 10.5.1: Forms and Point Groups is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Dexter Perkins via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.