The cinquefoil knot is a torus knot. Meaning, it can be drawn as a curve winding around a torus.
We can deform a torus m_n_knot with the help of the inside-out-deformation
of the Clifford torus
[see Clifford Torus]
into a torus n_m_knot. We only need to place the knot in such a way on the torus
that the torus point, which passes through infinity under the inside-out deformation,
does not lie on the knot.
In the animation the knot is realized as a strip on the torus by restricting a suitable
parametrization to a narrow band.