This tiling is a generalization of the Godreche-Lancon-Billard Binary first derived by T. Hibma and later worked out in detail by S. Pautze.
All interior angles are integer multiples of `$\frac{\pi}{n}$`

.
For `$n=5$`

it is identical to the Godreche-Lancon-Billard Binary tiling with 2 prototiles.
For odd `$n$`

it has `$\frac{n-1}{2}$`

prototiles.
For even `$n$`

it has `$n+1$`

prototiles.
The inflation multiplier is `$\sqrt{2 + 2 \cos(\frac{\pi}{n})}$`

.
The example shown below is the tiling for `$n=9$`

.

[Pau2017]

Pautze, S

**Cyclotomic aperiodic substitution tilings**

*Symmetry*
2017,
9(2),
doi.org/10.3390/sym9020019

[Hib2015]

T. Hibma

**Generalization of Non-periodic Rhomb Substitution Tilings**

*arXiv*
2015,
https://arxiv.org/abs/1509.02053