What Are the Three Types of Symmetry?

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The three main types of symmetry used in mathematics are reflectional symmetry, rotational symmetry and point symmetry. Other less common types of symmetry include translational symmetry, glide symmetry, helical symmetry and symmetry of scale.

Reflectional symmetry, sometimes called mirror or line symmetry, occurs when an image can be flipped around an axis and still appear the same. For example, the letter “V” can be flipped 180 degrees around a central vertical axis and still look identical, while the letter “B” cannot. A rotationally symmetrical object remains the same after being rotated around a central point. A circle has rotational symmetry if rotated any number of degrees, whereas a square has rotational symmetry only if rotated some multiple of 90 degrees in any direction. Point symmetry occurs when every point of an image has a matching point that is the same distance from the central point but in the opposite direction. For example, every point that is at the top right has a corresponding point at the bottom left.