Self-affine convex polygons

A polygon in ${{mathbb R}^2}$ is called self-affine if it can be dissected into k ≥ 2 affine images of itself. Self-affine convex polygons have at most five vertices. Triangles are trivially self-affine. It is shown that every convex quadrangle is self-affine, whereas only some, but not all convex pentagons are self-affine.