  We extend the classical Domino problem to any tiling of rhombus-shaped tiles.
For any subshift X of edge-to-edge rhombus tilings, such as the Penrose
subshift, we prove that the associated X-Domino problem is $\Pi^0_1$ -hard and
therefore undecidable. It is $\Pi^0_1$ -complete when the subshift X is given
by a computable sequence of forbidden patterns.
