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