  We consider the Morse coding of the geodesic flow on the hyperbolic plane $H$
with respect to a Dirichlet fundamental domain $D$ of a Fuchsian group
$\Gamma$. The main theorem states that the codes of all the generic geodesics
constitute a $k$-step topological Markov chain, if and only if the fundamental
domain $D$ is an ideal polygon (i.e. has all of its vertices on the absolute).
