{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07592",
  "author_total": 3,
  "authors": [
    {
      "name": "Marianne Imperor-Clerc"
    },
    {
      "name": "Jean-Francois Sadoc"
    },
    {
      "name": "Simon Tatham"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9v7rp1m8zjhqw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07592",
  "fulltext_url": null,
  "id": "9v7rp1m8zjhqw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07592",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2505|Quasicrystal Structures and Properties"
    ]
  ],
  "openalex": "W7212084660",
  "pdf_url": "https://arxiv.org/pdf/2609.07592",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9v7rp1m8zjhqw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.07592",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07592"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Chasing rotational symmetry in the spectre tiling",
  "title_text": "Chasing rotational symmetry in the spectre tiling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/9v7rp1m8zjhqw",
  "venue": "arXiv",
  "versions": []
}