  We state and prove a corrected version of a theorem of Singerman, which
relates the existence of symmetries (anticonformal involutions) of a
quasiplatonic Riemann surface $\mathcal S$ (one uniformised by a normal
subgroup $N$ of finite index in a cocompact triangle group $\Delta$) to the
properties of the group $G=\Delta/N$. We give examples to illustrate the
revised necessary and sufficient conditions for the existence of symmetries,
and we relate them to properties of the associated dessins d'enfants, or
hypermaps.
