Also known as ‘table tiling’. In [Sol97] was shown that its dynamical spectrum has a continuous component. Thus it cannot be a cut and project tiling. The same was shown in [Rob99] , where a topological model of the dynamical system of the domino tilings is obtained.
Robinson, E. Arthur, Jr.
On the table and the chair
Indag. Math. (N.S.) 1999, 10, 4, pp. 581--599, MR1820555