Watanabe Ito Soma 12-fold

Discovered by


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. Thank you!

Watanabe Ito Soma 12-fold (variant) is another version of this rule with more symmetry.

Substitution Rule

Rule Watanabe Ito Soma 12-fold


Patch Watanabe Ito Soma 12-fold download vectorformat Watanabe Ito Soma 12-fold


Watanabe, Y and Soma, T and Ito, M
A new quasiperiodic tiling with dodecagonal symmetry
Acta Crystallogr. 1995, A51, pp. 936--942,