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 S (one uniformised by a normal
subgroup N of finite index in a cocompact triangle group Δ) to the
properties of the group G=Δ/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