Figure-eight knot

Example

The figure-eight knot is the knot obtained by closing up the figure-eight knot of rope. Its standard diagram has $4$ crossings that alternate over and under along the curve. One parametrization of it is $$t \mapsto \bigl((2 + \cos 2t) \cos 3t, \ (2 + \cos 2t) \sin 3t, \ \sin 4t\bigr), \qquad t \in [0, 2\pi).$$ Its crossing number is $4$. Indeed, the only knots with crossing number less than $4$ are the unknot and the two trefoils, and the figure-eight knot is neither.