Which Shapes Have Rotational Symmetry?

By Staff WriterLast Updated Apr 9, 2020 12:52:54 PM ET
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Shapes with points that are evenly positioned around a central point have rotational symmetry. Rather than being found in a standard geometric object, shapes that have geometric symmetry are typically combinations of different shapes.


An object is said to have rotational symmetry if it looks that same after being turned slightly. One shape that has full rotational symmetry is a circle. Regardless of how a circle is turned, it always appears the same.

For other objects, the amount of rotational symmetry varies. A star with five equally-spaced legs has five-fold rotational symmetry. The degree of rotation can be found by dividing 360 degrees by the folds of rotational symmetry. Therefore, a star has 72 degrees of rotational symmetry.

Examples of rotational symmetry are found in everyday life. Returning to the example of a star, a five-legged starfish follows the same rules. Another common example of rotational symmetry in nature is the flower. Depending on the type of flower, there can be many folds of rotational symmetry.

Rotational symmetry can also be affected by color. An example of this is the yin-yang symbol. If the difference in color between the two halves is neglected, then this symbol has two-fold symmetry and can be turned 180 degrees and appear the same.