Self-affine convex discs are polygons (Q664215)

A set \(D \subset \mathbb R^{2}\) is a convex disc if it convex and compact and its interior int \(D\) is non-empty. A convex disc \(D\) is called self-affine if it can be dissected into \(m \geq 2\) affine images of itself. The author obtains the following results: every self-affine convex disc \(D\) is a polygon and \(D\) must be a triangle, a quadrangle or a pentagon.