• 1 École normale supérieure de Lyon

In this article, we study the question of tilings on a hexagon mesh with balanced 3-tiles. This problem has been studied by Conway and Lagarias in [CL90], by studying the tiling groups, in fact a group containing the tiling-groups, and their Cayley graphs. We will use two different approaches. The first one is based on matchings in bipartite graphs, which in this case are in correspondance with tilings of domains by lozenges, and thus can be efficiently studied, using Thurston's algorithm (see [Thu90]). The second one is based on a color and balancing approach of Thurston's algorithm, exposed in [Fou96].