  One-vertex maps (a type of dessin d'enfant) give a uniform characterization
of certain well-known algebraic curves, including those of Klein, Wiman,
Accola-Maclachlan and Kulkarni. The characterization depends on a new
classification of one-vertex (dually, one-face or unicellular) maps according
to the size of the group of map automorphisms. We use an equivalence relation
appropriate for studying the faithful action of the absolute Galois group on
dessins, although we do not pursue that line of inquiry here.
