Regular polygonal systems

Abstract

Let M = M(Ω) be any triangle-free tiling of a planar polygonal region Ω with regular polygons. We prove that its face vector f(M) = (f₃, f₄, f₅, …), its symmetry group S(M) and the tiling M itself are uniquely determined by its boundary angles code c_a(M) = c_a(Ω) = (t₁, …, t_r), a cyclical sequence of numbers t_i describing the shape of Ω.