Fullerenes and dessins d'enfants

Fullerenes, being a hot point of modern chemistry and several theoretical sciences, have lots of applications, ranging from quantum computers to medicine.
The mathematical aspects of the fullerenes theory are also diverse. Various fullerenes-related topics of graph theory, finite groups and their representations, geometry of polytopes, isoperimetric problems, etc., can be found in many current papers. The talk is aimed at the considerations of yet another mathematical discipline, the theory of dessins d’enfants, that, hopefully, can promote the understanding of combinatorics and geometry of fullerenes.
The basics of dessins d’enfants theory will be introduced and the calculations related to one of the simplest cases presented.