Asymmetric Propeller Generalized to Similar Polygons

Summary: The original propeller problem states that if three equilateral triangles have a common vertex, then the midpoints of the three segments connecting the other six vertices always form another equilateral triangle. The result also applies to three similar triangles. In order to further generalize it to similar polygons, we use quadrilaterals to show in general that the new polygon must be constructed from the centroids of the corresponding vertices of the old ones.