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What are the types of symmetry on a flat plane?

Updated: 8/18/2019
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LinJRichard

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13y ago

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Rotational symmetry, such as rotating an n-sided regular polygon through angles of 360k/n degrees (2kPI/n radians) about the centre (k is an integer)

Reflectional symmetry, where each point perpendicular to a given axis of symmetry at a distance D say, is reflected to the other side of the axis at the point again a distance D from the axis.

Translational symmetry. The best examples of such symmetries are sine or cosine curves which are translated a distance 360k degrees (2PI radians) along the x-axis. Tiling patterns are other examples

All other types of symmetries in the plane are compositions of the above three.

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Q: What are the types of symmetry on a flat plane?
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