Figure-eight knot group ($⟨a,b\mid a{b}^{-1}{a}^{-1}ba=ba{b}^{-1}{a}^{-1}b⟩$)

The fundamental group of the figure-eight knot complement has the displayed two-generator one-relator presentation. It follows from the Artin automorphism of a braid for $({\sigma }_1{\sigma }_2^{-1}{)}^2$ by eliminating the third meridian from its fixed-generator presentation.