  We consider a specific %piecewise rotation of the plane that is continuous on
two half-planes, class of piecewise rotations of the plane that are continuous
on two half-planes, as studied in \cite{Bosh.Goet.03}, \cite{Goet.Quas.09} and
\cite{Che.Goe.Qua.12}. %If Assuming that the angle belongs to the set
$\{\frac{\pi}{2},\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{4}\} %$ $, we give a
description of the symbolic dynamics of this map in the bijective symmetric
case.
