Schaad's 7-fold
Schaad’s 7-fold is a progressions of Madison’s 7-Fold and so it shares many properties with it. It is a tiling with 7-fold symmetry and a lot of locally 7-fold symmetric patches. There are three tile shapes, but only eight instead nine different prototiles. The inflation factor is a PV number: $2+2\cos\left(\frac{\pi}{7}\right)+2\cos\left(\frac{2\pi}{7}\right) = 5.04891733952231\ldots$ which is the largest root of $x^{3}-6x^{2}+5x-1$.

Polytopal Tiles
Self Similar Substitution
Finite Local Complexity
Rhomb Tiles
Finite Rotations