Tiling Convex Polygons With Triangle(π/6,π/6,(2π)/3)

Let Pn be a plane convex polygon with n vertices.We say that Pn is tiled with triangles△₁,△₂,...,△m if Pn=△₁∪△₂∪...∪△m and the interiors of△₁,△₂,...,△m are mutually disjoint.Triangles△_i（i = 1,...,m）are called the tiles of the tiling.We say that A congruently tiles Pn if each tile △_i（i = 1,....,m）is congruent with △.In this paper we study the set T= {（n,κ）:n ∈ {3,4,5,...}κ∈{1,2,3,...},and there exists a convex n-gon that can be tiled with k congruent triangles（π/6，π/6，2π/3）} If a convex n-gon can be dissected into congruent triangles of angles π/6，π/6，2π/3,then n ∈{3,4,5,6,7,8,9,10,11,12}.Denote T_n = {κ:（n,k）∈T}（n = 3,4,5,6,7,8,9,10,11,12）,so T and T_n are identifying.In the text,we consider the problem of tiling convex n-gon（n = 3,4,5,6,7,8,9,10,11,,12）with congruent triangles（π/6，π/6，2π/3）and get the number of tiles.