A tiling T of the Euclidean plane (E2) is a countable collection of closed topological disks called tiles T = {Ti : i ∈ N} that is a covering (Ui Ti = E2) as well as a packing (Int(Ti) ∩ Int(Tj) = ∅ if i ̸= j, Int(T) denotes the interior of tile T). One of the problems of interest in discrete geometry is the classification of tilings based on transitivity properties of their vertices, edges and tiles. This talk presents a family of tilings whose vertices, edges and tiles have exactly a, b and c orbits, respectively, under the action of its symmetry group. Such tilings are called (a, b, c) tilings. Starting from the regular tiling of E2 by triangles or hexagons with symmetry group G, we introduce a method for constructing (a, b, c) tilings. We derive formulas for the admissible values of a, b and c that can occur for (a, b, c) tilings with a prescribed symmetry group H ≤ G.