  The recently suggested tangle calculus for knot polynomials is intimately
related to topological string considerations and can help to build the
HOMFLY-PT invariants from the topological vertices. We discuss this interplay
in the simplest example of the Hopf link and link $L_{8n8}$. It turns out that
the resolved conifold with four different representations on the four external
legs, on the topological string side, is described by a special projection of
the four-component link $L_{8n8}$, which reduces to the Hopf link colored with
two composite representations. Thus, this provides the first explicit example
of non-torus link description through the topological vertex. It is not a real
breakthrough, because $L_{8n8}$ is just a cable of the Hopf link, still, it can
help to intensify the development of the formalism towards more interesting
examples.
