Crystallography Picture Book - Fullerenes by S. Weber

By S. Weber

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Crystal Classes There are 32 crystal symmetry classes, each characterized by a point group. They comprise the symmetry elements Rand R, taken either singly or in combination, with R restricted to the values 1, 2, 3, 4, and 6. 33 shows. 5. We shall not be concerned here to derive the crystallographic point groups-and there are several ways in which it can be done*-but to give, instead, a scheme which allows them to be worked through simply and adequately for present purposes. The symbols for rotation and reflection are similar to those used in two dimensions.

2 lists them all. 34a shows a stereogram for point group m. The inverse diad is lying normal to the m plane. A consideration of the two operations in • See Bibliography (Ladd). 33. Sections of threedimensional figures and the rotational symmetries of their smallest structural units; (a)-(d) are space-filling patterns. lOa). 1 CRYSTAL GEOMETRY. 2. L projection • II projection or inclined to projection projection • II projection projection 0 lJ. L projection ( II projection " R is equivalent to R plus i only where R is an odd number: i represents the center of symmetry, but 2, 4, and 6 are not centrosymmetric point groups.

27f). 27 has a symmetry pattern that can be described by a two-dimensional point group, and it is convenient to illustrate these point groups by stereograms. 27. Two-dimensional objects and their point groups. The motifs are built up from the asymmetric unit (a), by operating on it according to the point-group symbol. Note that the symmetry element must intersect the asymmetric unit, and has been set at the uppermost part of (a). grams for the two-dimensional point groups 1,2,3,4,6, and m. It should be noted that in using stereogram-like drawings to illustrate twodimensional symmetry, the representative points (poles) are placed on the perimeter; such situations may represent special forms (page 40) on the stereograms of three-dimensional objects.

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