  We consider a specific piecewise rotation of the plane that is continuous on
two half-planes, as studied by some authors like Boshernitzan, Goetz and Quas.
If the angle belongs to the set
$\{\frac{\pi}{2},\frac{2\pi}{3},\frac{\pi}{4}\}$, we give a complete
description of the symbolic dynamics of this map in the non symmetric bijective
case.
