Nontorus link from topological vertex

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 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.