Achiral and Chiral Knots

A chiral knot is a knot that is not equivalent to its mirror image. If a knot is equivalent to its mirror, then it is called achiral. This animation first shows two views of the Figure-8 knot. The left knot is rotated by a quarter turn and we can see the two appear to be mirror images (reflecting in the plane of the screen). This is a proof that the Figure-8 knot is achiral.

We then see an example of a chiral knot, the trefoil. One is a mirror image of the other. We rotate one by a half turn and they are still mirror images. While this is not a proof that the trefoil is chiral, it is enough to be convincing.

To try this animation yourself, download KnotPlot from


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