Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. A non-invertible knot is any knot which does not have this property. The invertibility of a knot is a knot invariant. An invertible link is the link equivalent of an invertible knot.

There are only five knot symmetry types, indicated by chirality and invertibility: fully chiral, reversible, positively amphichiral noninvertible, negatively amphichiral noninvertible, and fully amphichiral invertible.^[1]

^ Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first 1,701,936 knots" (PDF), The Mathematical Intelligencer, 20 (4): 33–48, doi:10.1007/BF03025227, MR 1646740, S2CID 18027155, archived from the original (PDF) on 2013-12-15.

[htw-1] Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first 1,701,936 knots" (PDF), The Mathematical Intelligencer, 20 (4): 33–48, doi:10.1007/BF03025227, MR 1646740, S2CID 18027155, archived from the original (PDF) on 2013-12-15.

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