Y. Watanabe

Discovered Tilings

Preview Watanabe Ito Soma 12-fold (variant)
Watanabe Ito Soma 12-fold (variant)

This is a variant of Watanabe Ito Soma 12-fold, with more symmetry.

Finite Rotations Polytopal Tiles

Preview Watanabe Ito Soma 12-fold
Watanabe Ito Soma 12-fold

The source of the tiling can be found in [WSI95] Fig. 2 (iii) and Fig. 3. Its inflation factor is $2+\sqrt{3}$ and it has finite local complexity with respect to rigid motions. Unfortunately the corresponding substitution rules given in Fig. 2 (iii) of the paper are not unique. For some time the exact substitution rules which generate the square level-3-supertile in Fig. 3 of the paper remained unclear. Finally Alessandro Musesti and Maurizio Paolini submitted the correct set of substitution rules in January 2023 to us.

Finite Rotations Polytopal Tiles Self Similar Substitution Finite Local Complexity

Preview Watanabe Ito Soma 8-fold
Watanabe Ito Soma 8-fold

This tiling was originally introduced in [WSI87] , however the description given there admits several substitution rules. This is the version given explicitly in [WSI95] . This is an example of a cut and project with a mixed internal space, a product of Euclidean and $p$-adic spaces, namely $\mathbb{R}^2 \times \mathbb{Q}_2$.

Finite Rotations Model Set Rhomb Tiles Polytopal Tiles Self Similar Substitution Finite Local Complexity