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More Poly-Polygon Portals.

So let’s say a polygon has a spiral for a point on it’s border if there’s a center so that a rotation + dilation takes a vertex to that point and each other vertex to a point on a corresponding edge. (Then the next dilation + rotation will have the same property, etc.) Squares have spirals, and rectangles. Any others? Most quadrilaterals seem to have points that do not have spirals, but do most quads have points that do have spirals? No idea. Yet.

Playing around, it seems to depend on the point on the boundary, and I’m guessing the answer is not every polygon has a spiral. For the ones that do, the location of the center seems interesting.

If anyone wants the GeoGebra for this, let me know and I’ll upload. Interested?