Self-similar aperiodic patterns with 9-fold symmetry (Q2347034)

In the paper at hand, H. J. Rivertz constructs aperiodic tilings with 9-fold symmetry. It consists of four different tiles; the regular hexagon and the rhombi with angles \(20^\circ\), \(40^\circ\) and \(80^\circ\). To construct this tiling, Rivertz generalizes a cut-and-project method due to Penrose: Find a suitable two-dimensional subspace \(E\) in \(\mathbb{R}^9\) and consider the strip \(\Sigma=E+(0,1)^9\). Projecting the integer points \(\Sigma\cap\mathbb{Z}^9\) on \(E\) yields the vertices of the tiling. Penrose's construction was originally applied to 5-fold symmetries, and certain details of the construction need to be adapted to dimension \(n=9\).