  We outline a project to study the Galois action on a class of modular graphs
(special type of dessins) which arise as the dual graphs of the sphere
triangulations of non-negative curvature, classified by Thurston. Because of
their connections to hypergeometric functions, there is a hope that these
graphs will render themselves to explicit calculation for a study of Galois
action on them, unlike the case of a general dessin.
