From the viewpoint of gluing theory, it is convenient to regard the boundary marked points of the holomorphic polygons as punctures, where the Riemann surface structure is locally modelled on strip like ends. The moduli of abstract holomorphic polygons with $k+1$ marked points has a compactification known as the Stasheff associahedron $\overline{\mathcal{R}}_{k+1}$. On account of the geometric picture of polygons in $\mathbb{R}^{2}$, we often refer to the strip like ends as corners.