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Inversion is perhaps the most difficult of the simple symmetry operations to visualize. Inversion involves the repetition of motifs by inversion through a point called a center of inversion (i). Inversion occurs when every component of a pattern is repeated by equidistant projection through a common point or center of inversion. The two “letters” in Figure 4.5 illustrates this enantiomorphic symmetry operation and shows the center through which inversion occurs. In some symbolic notations centers of inversion are symbolized by (c) rather than (i).

Figure 4.5 Inversion through a center of symmetry (i) illustrated by the letter “m” repeated by inversion through a center (inversion point).

One test for the existence of a center of symmetry is that all the components of a pattern are repeated along straight lines that pass through a common center and are repeated at equal distances from that center. If this is not the case, the pattern does not possess a center of symmetry.

Figure 4.6 (a) Mirror plane (m) with the translation vector (t), contrasted with (b) a glide plane (g) with the translation vector (t/2) combined with mirror reflection.