If a knot is viewed as the oriented diffeormorphism class of an oriented pair, K = (S
Of course a knot possessing any two of these types of symmetry has all three. Thus, in the table, a knot is called reversible if that is the only symmetry it has. Similarly for negative amphicheiral. If it has none of these symmetries it is chiral, and if it has all three it is called fully amphicheiral.
It should be pointed out that for prime knots with less than 12 crossings, all amphicheiral knots are negative amphicheiral.