Girih inspired 14-fold Tiling
A tiling resembling Islamic Girih patterns but using 14-fold symmetry rather than 8- or 10- or 12-fold. Its inflation factor is $1 + \cos(\frac{\pi}{14}) \csc(\frac{\pi}{7}) + 2 \cos(\frac{3 \pi}{14}) \csc(\frac{\pi}{7}) = 6.850855...$ which is a PV number. It uses 11 prototiles altogether, 10 of them showing $D_2$-symmetry and one showing $D_{14}$-symmetry. This shows that all resulting tilings have local patches with 14-fold symmetry, and that the hull contains tilings with global 14-fold symmetry.