Читать книгу Earth Materials - John O'Brien - Страница 96

As discussed earlier, any fundamental unit of two‐dimensional pattern, or motif, can be repeated by various symmetry operations to produce a larger two‐dimensional pattern. All two‐dimensional motifs that are consistent with the generation of long‐range two‐dimensional arrays can be assigned to one of ten plane point groups based on their unique plane point group symmetry (Figure 4.8). Using the symbolic language discussed in the previous section on symmetry, the ten plane point groups are 1, 2, 3, 4, 6, m, 2mm, 3m, 4mm, and 6mm. The numbers refer to axes of rotation that are perpendicular to the plane (or page); the m refers to mirror planes perpendicular to the page. The first m refers to a set of mirror planes that is repeated by the rotational symmetry and the second m to a set of mirror planes that bisects the first set. Note that the total number of mirror planes is the same as the number associated with its rotational axis (e.g., 3m has three mirror planes and 6mm has six mirror planes).