Girih inspired 14-fold Tiling

• Finite Local Complexity (FLC)
• Finite Rotations
• Girih
• Polytopal Tiles
• Self-Similar Substitution

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

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References

[Pau2017]
Pautze, S
Cyclotomic aperiodic substitution tilings
Symmetry 2017, 9(2), doi.org/10.3390/sym9020019

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