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arXiv · 2609.07592

Chasing rotational symmetry in the spectre tiling

Marianne Imperor-Clerc·Jean-Francois Sadoc
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Abstract

We identify the rotational symmetry centers in the spectre tiling. We find that both 2-fold and 3-fold symmetry centers are coexisting. Local and global symmetry operations are distinguished. The link between substitution schemes and rotational symmetry is investigated. We introduce a set of three finite patterns, named diabolo, 2-arms and 3-arms, in order to visualize rotational symmetry in the spectre tiling. Using these three patterns, we propose geometrical constructions for generating patches of the spectre tiling with 2-fold and 3-fold global rotational symmetry.

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Marianne Imperor-Clerc, Jean-Francois Sadoc. 2026-09-07. Chasing rotational symmetry in the spectre tiling. https://arxiv.org/abs/2609.07592

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