  In this paper we obtain a classification of rigid isotopy classes of totally
reducible trigonal curves lying on a Hirzebruch surface $\Sigma_n$, and having
a maximal number of non-degenerated double points. Such curves correspond to
morsifications of a totally real semiquasihomogeneous singularity of weight
$(3,3n)$ (the union of three smooth real branches intersecting each other with
multiplicity $n$). We obtain this classification by studying combinatorial
properties of dessins.
  In the appendix, we prove that any morsification of a totally real
semiquasihomogeneous singularity of weight $(3,3n)$ can be realized (up to
isotopy) by the restriction of the equation to the Newton diagram and adding
monomials under the Newton diagram.
