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Template:Knot chirality

Chiral Amphichiral
Invertible Reversible Fully amphichiral
Non-invertible Fully chiral Amphichiral
Documentation icon Template documentation

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]


  1. Hoste, Jim; Thistlethwaite, Morwen; Weeks, Jeff (1998), "The first 1,701,936 knots", The Mathematical Intelligencer 20 (4): 33–48, MR 1646740, doi:10.1007/BF03025227 .