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We describe a procedure that creates an explicit complex-valued polynomialfunction of three-dimensional space, whose nodal lines are the three-twist knot$5_2$. The construction generalizes a similar approach for lemniscate knots: abraid representation is engineered from finite Fourier series and thenconsidered as the nodal set of a certain complex polynomial which depends on anadditional parameter. For sufficiently small values of this parameter, thenodal lines form the three-twist knot. Further mathematical properties of thismap are explored, including the relationship of the phase critical points withthe Morse-Novikov number, which is nonzero as this knot is not fibred. We alsofind analogous functions for other knots with six crossings. The particularfunction we find, and the general procedure, should be useful for designingknotted fields of particular knot types in various physical systems.

Constructing a polynomial whose nodal set is the three-twist knot $5_2$