Polygonal attractors are parallelepipeds

Let $d$ be a positive integer, and let an attractor in $\mathbb{R}^d$ be a polygonal set, not necessarily convex.

Polygonal-attractor conjecture. Every, not necessarily convex, attractor in $\mathbb{R}^d$ which is a polygon is a parallelepiped.

The paper proves the corresponding statement in the plane for nonconvex polygons, while the higher-dimensional case is presented as a conjectural generalization.