Discovered Tilings
A substitution rule that gives rise to a non-periodic tiling $\mathcal{T}_{17}$ with $17$-fold dihedral symmetry. The substitution factor is $\mu_{17}=1/(2\sin(\pi/34))$.
The tiling $\mathcal{T}_{17}$ is obtained by assigning orientations to relevant tiles in the 1-order supertiles to ensure the …
Finite Rotations Polytopal Tiles Self Similar Substitution Generalized Robinson Triangles
The substitution rule is similar to Say-awen 17-fold. It is invariant under $21-$fold dihedral symmetry and has infinite local complexity. The substitution factor is $\mu_{21}=1/(2\sin(\pi/42))$, which is non-Pisot with minimal polynomial $p_{21}(x)=x^6-8x^5+8x^4+6x^3-6x^2-x+1$.
Finite Rotations Polytopal Tiles Self Similar Substitution Generalized Robinson Triangles
A substitution rule that gives rise to an aperiodic tiling with dense tile orientations and 5-fold rotational symmetry. The inflation factor is $\sqrt{6+\sqrt{5}}$. The tiling has finite local complexity with respect to rigid motions.
Finite Local Complexity Polytopal Tiles Self Similar Substitution Infinite Rotations