Self-affinity of every non-convex quadrangle

Determine whether every non-convex quadrangle is self-affine, meaning that it admits a dissection into finitely many affine images of itself.

Background

The paper proves that for every integer n greater than or equal to 3, there exists an n-self-affine non-convex quadrangle, and that no non-convex quadrangle is 2-self-affine. These existence and nonexistence results do not determine whether an arbitrary non-convex quadrangle is self-affine for some number of pieces.