Stefan Pautze
Discovered Tilings
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 …
Finite Rotations Polytopal Tiles Parallelogramm Tiles Rhomb Tiles Finite Local Complexity
The FASS-curve of the pentagon bases on an aperiodic substitution tiling with four substitution rules and appropriate decorations.
The substitution tiling was derived from the Robinson Triangle Tiling.
Its inflation factor is the golden mean $\frac{\sqrt{5}}{2} + \frac{1}{2} = 1.618033988\ldots$.
Polytopal Tiles Self Similar Substitution With Decoration FASS_curve
10-fold cyclotomic aperiodic tiling with dense tile orientations (CAST DTO).
Finite Local Complexity Polytopal Tiles Self Similar Substitution Infinite Rotations
8-fold cyclotomic aperiodic tiling with dense tile orientations (CAST DTO).
Finite Local Complexity Polytopal Tiles Self Similar Substitution Infinite Rotations
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 …
Finite Local Complexity Finite Rotations Polytopal Tiles Self Similar Substitution Girih