  In the last section of \cite{CompHyp} it is proved that the map $\mathcal{I}$
is a finite-sheeted covering map between $\mathcal{P}$ and $\mathcal{M}$. As
$\mathcal{M}$ is simply connected it is deduced that $\mathcal{I}$ is a
homeomorphism. The fact that $\mathcal{P}$ is connected is missing. Here we
provide a proof.
