Penrose tiling rotating in the five dimensional space

The lift of a Penrose tiling is a digitalization of a two-dimensional plane in the five-dimensional Euclidean space. We here rotate such a lift in order to show its shadows, i.e., its projections onto the three-dimensional spaces generated by three of the five vectors of the canonical basis. Each of these ten shadows has a direction of periodicity (whereas one can see along other directions Sturmian words defined by the golden ratio). The slope of the plane that digitalizes this Penrose tiling is uniquely characterized by the periodicities of these shadows.