Ball-homeomorphism conjecture for the twindragons B and C

The twindragons $\mathcal B$ and $\mathcal C$ are self-affine tiles in the plane. Ball-homeomorphism conjecture. The twindragons $\mathcal B$ and $\mathcal C$ are homeomorphic to a ball. The preceding discussion shows that these are the only two twindragons that could still have the structure of a polyhedron, although the authors expect that this is not quite the case; the ball-homeomorphism claim is presented as an expectation and is not established here.