Similar Polyfetts Tiling a Square

A polyfett or polifetto is a plane figure formed by joining equal isosceles right triangles on the square grid along equal edges and at corners. It is a generalization of a polyabolo.

A few polyfetts can form a square by joining variously sized copies of themselves. Here I show some examples.

The tilings shown use as few tiles as I know how, and are not necessarily unique under this condition. If you find a tiling with fewer tiles, please write.

Only polyfetts that are not polyaboloes are shown here. See also Similar Polyaboloes Tiling a Square.