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.
[Sol97]
Solomyak, B
Dynamics of self-similar tilings.
Ergodic Theory Dynam. Systems
1997,
17, 3,
pp. 695--738,
[Rob99]
Robinson, E. Arthur, Jr.
On the table and the chair
Indag. Math. (N.S.)
1999,
10, 4,
pp. 581--599,
MR1820555