Alex Madison
Discovered Tilings
Madison's 7-fold
A tiling with 7-fold symmetry and a lot of locally 7-fold symmetric
patches. There are only three tile shapes, but 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