A topological group action of a finite group encodes the information of the symmetries of a surface. One can study these actions by analyzing their orbit spaces. A surface with a topological group action whose orbit space is a sphere with three branch points is called a quasiplatonic surface. These quasiplatonic surfaces generalize the main characteristics of the Platonic solids, including their discreteness. We discuss the link between the number of quasiplatonic topological actions of the cyclic group and the number of bipartite maps (i.e., regular dessins d'enfants) with a cyclic group of symmetries.