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Reflection is as familiar to us as our own reflections in a mirror or that of a tree in a still body of water. It is also the basis for the concept of bilateral symmetry that characterizes many organisms (Figure 4.4). Yet it is a symmetry operation that is somewhat more difficult for most people to visualize than rotation. Reflection is a symmetry operation in which every component of a pattern is repeated by reflection across a plane called a mirror plane (m). Reflection occurs when each component is repeated by equidistant projection perpendicular to the mirror plane. Reflection retains all the components of the original motif but changes its “handedness”; the new motifs produced by reflection across a mirror plane are mirror images of each other (Figure 4.4). Symmetry operations that change the handedness of motifs are called enantiomorphic operations.

Figure 4.4 Two‐ and three‐dimensional motifs that illustrate the concept of reflection across a plane of mirror symmetry (m). (a) Mirror image of the letter “R”. (b) Bilateral symmetry of a butterfly; the two halves are nearly, but not quite, perfect mirror images of each other.

Source: Image from butterflywebsite.com. © Mikula Web Solutions.

One test for the existence of a mirror plane of symmetry is that all components of the motifs on one side of the plane are repeated at equal distances on the other side of the plane along projection lines perpendicular to the plane. If this is not true, the plane is not a plane of mirror symmetry.