On the topology of cycles in pseudolinear programs

By demand coming from the quasicrystal community, we present here a construction realizing an arbitrary oriented link in $\mathbb R^3$ by the graph of a 3d pseudolinear (or matroid) program. This gives a hint about possible “topological complexity” of rank 4 oriented matroids $\approx3d$ pseudoplane arrangements $\approx3d$ quasicrystal tilings.