Watanabe Ito Soma 8-fold

Discovered by


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 $\mathbb{R}^2 \times \mathbb{Q}_2$.

Substitution Rule

Rule Watanabe Ito Soma 8-fold


Patch Watanabe Ito Soma 8-fold


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

Watanabe, Y and Soma, T and Ito, M
Nonperiodic tessellation with eightfold rotational symmetry
Acta Crystallogr. 1987, A43, pp. 133--134,

Watanabe, Y. and Ito, M. and Soma, T. and Betsumiya T.
Nonperiodic Tesselation with Eight-fold Rational Symmetry
In Science on Form: Proceedings of the First International Symposium for Science on Form; Ishizaka, S., Kato, Y., Takaki, R., Toriwaki, J., Eds.; KTK Scientific Publishers: Tokyo, Japan 1986, pp. 471-477,