Figure 3.

Reduced diagrams and writhe: a) Definition of a negative and a positive crossing. b) A knot can be oriented by following its loop in an arbitrary direction. In the depicted orientation, the shown trefoil knot has a writhe (Wr) of 3, as all three crossings are positive. The orientation can be reversed by rotation along the indicated C₂‐axis. c) In a trefoil knot with nugatory crossings, the writhe can take any value. Knot diagrams without nugatory crossings are referred to as “reduced”.