Sheel structure of dodecagonal quasicrystals associated with root system F₄ and cyclotomic field Q(ζ₁₂)

Abstract

Using a Coxeter transformation of type F₄, we will construct quasicrystals of dimension 2 with twelvefold symmetry. Then, such quasicrystals will be realized as subsets of a certain cyclotomic field. And we will study a typical shell structure algebraically. In particular, we can give its mathematical meaning in terms of elementary number theory.

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Notes on contributors

Jun Morita

Kuniko Sakamoto