Invariants of links and knots on $T$-polyhedra

Any link in $\mathbb R^3$ can be isotopically deformed to the polyhedron $T=\{(x,y,z)\in\mathbb R^3\mid z=0$ or $y=0$, $z\ge0\}$. Arising nontrivial theory of links and knots on $T$ is developed. The main result consists in presenting an isotopic invariant, which can distinguish pairs of knots on $T$ isotopic as knots in $\mathbb R^3$.