PreprintCC BY-SA 4.0arXiv
Chasing rotational symmetry in the spectre tiling
Abstract
We identify the rotational symmetry centers in the spectre tiling. We find that both 2-fold and 3-fold symmetry centers are coexisting, with two different types of 3-fold centers. Local and global symmetry operations are distinguished, and characterized in terms of substitution systems. We introduce a decomposition of the spectre tiling in terms of three metatiles named diabolo, 2-arms and 3-arms, valid at any substitution level. We propose geometrical constructions for generating patches of the spectre tiling with 2-fold and 3-fold global rotational symmetry.
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BibTeX
@misc{imperorclerc2026chasing,
title = {{Chasing rotational symmetry in the spectre tiling}},
author = {Marianne Imperor-Clerc and Jean-Francois Sadoc and Simon Tatham},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.07592},
eprint = {2609.07592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07592},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Chasing rotational symmetry in the spectre tiling
AU - Marianne Imperor-Clerc
AU - Jean-Francois Sadoc
AU - Simon Tatham
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2609.07592
UR - https://arxiv.org/abs/2609.07592
AB - We identify the rotational symmetry centers in the spectre tiling. We find that both 2-fold and 3-fold symmetry centers are coexisting, with two different types of 3-fold centers. Local and global symmetry operations are distinguished, and characterized in terms of substitution systems. We introduce a decomposition of the spectre tiling in terms of three metatiles named diabolo, 2-arms and 3-arms, valid at any substitution level. We propose geometrical constructions for generating patches of the spectre tiling with 2-fold and 3-fold global rotational symmetry.
ER -