Generalization of interactions between finite symmetry elements

2 Generalization of interactions between finite symmetry elements 

Hints select a p)Tamid (1), rotate it (2), reflect both (4), rotate all (6), and reflect all (8). Numbers in parenthesis indicate the total number of different pyramids that should be present in the figure after each symmetrical transformation. 

So far we have enough evidence that when two symmetry elements interact, they result in additional symmetry element(s). Furthermore, when three symmetry elements interact, they will also produce derivative symmetry elements. For example, three mutually perpendicular mirror planes yield a center of inversion in a point, which is common for all three planes plus three two-fold rotation axes along the lines where any two planes intersect. However, all cases when more than two elements interact with one another can be reduced to the interaction of pairs. The most typical interactions of the pairs of symmetry elements and their results are shown in Table 1.6. 

First element Second element Derived element (major) Comments, examples 

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