A torus knot is one that can be drawn on the surface of a torus. Examples include the trefoil

and cinquefoil

knots.

Definition

A knot $K$ is said to be a torus knot if it can be embedded in the surface of a torus, that is, we have the map $K:{S}^{1}\to {\mathbb{R}}^{3}$ factors through the embedding of some torus ${T}_{1}\cong {S}^{1}\times {S}^{1}$ into ${\mathbb{R}}^{2}$;