Links on $T$-polyhedra: examples of Gusarov's cubic spaces

Any link in $\mathbb R^3$ is isotopic to a link lying on the union $T$ of three half-planes with common boundary line. In an earlier paper, the author developed a nontrivial theory of links and knots on $T$. In the present paper, the results are interpreted in the context of M. Gusarov's theory of invariants of finite degree (the theory of “cubic spaces”).