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A form of symmetry in which parts of an object appear the same as other parts, such that if you rotate the object by some amount, it looks like the same object. For example, this figure has two-fold rotational symmetry:
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By rotating the figure through 180 degrees, what you get looks like what you started with.

Objects with three-fold rotational symmetry, such as a triskelion, can be rotated in increments of 120 degrees, and appear the same. In general, if an object appears the same n times during a 360 degree rotation, it is said to have M-fold symmetry, where M = 360/n.

Note that figures with rotational symmetry do not necessarily exhibit reflection symmetry, although there exist figures with reflection symmetry that also show rotational symmetry. One example is a star shape.

To be more specific, any figure with M-fold symmetry will also have reflection symmetry when M is odd.


On a two-dimensional co-ordinate plane, two-fold rotational symmetry is also known as symmetry about the origin.

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