Girih inspired 14-fold Tiling
Discovered by
Info
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 unit but not 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.
Substitution Rule
Patch
download vectorformat Girih inspired 14-fold Tiling
References
[Pau2017]
Pautze, S
Cyclotomic aperiodic substitution tilings
Symmetry
2017,
9(2),
doi.org/10.3390/sym9020019