Millars n-fold
J. Millar discovered a set of tilings with patches of dihedral symmetry $D_2n$ and inflation multiplier $\sqrt{2 + 2 \cos(\frac{\pi}{n})}$, which is the same inflation multiplier as of the Generalized Godreche-Lancon-Billard Binary. All interior angles of all prototiles are integer multiples of $\frac{\pi}{n}$. All prototiles have sides with unit length. All tilings have a prototile in the shape of a rhomb with interior angle $\frac{\pi}{n}$. The longer diagonal also defines the inflation multiplier.

Finite Rotations
Polytopal Tiles
Finite Local Complexity