{
  "abstract": "We classify all periodic tilings with a monotile known as R1 and called here the undertile, which underlies several aperiodic monotiles such as the Taylor-Socolar one. The classification is done using deflation, through a study of fracture lines between zones where deflation can be performed. A full classification of fracture patterns is given, that also applies to nonperiodic tilings with the undertile. This can be used to reprove nonperiodicity of some existing monotiles based on the undertile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20663",
  "author_total": 1,
  "authors": [
    {
      "name": "Arnaud Chéritat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74khnvx7x1mfz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20663",
  "fulltext_url": null,
  "id": "74khnvx7x1mfz",
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  "landing_url": "https://hal.science/hal-05802394v1",
  "language": "en",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mtrl-sci"
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      "math.CO"
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      "arxiv",
      "math.GT"
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      "openalex",
      "2505|Quasicrystal Structures and Properties"
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  "openalex": "W7222478944",
  "pdf_url": "https://hal.science/hal-05802394/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74khnvx7x1mfz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802394",
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      "url": "https://hal.science/hal-05802394v1"
    },
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.20663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20663"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Crystallization of the undertile",
  "title_text": "Crystallization of the undertile",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/74khnvx7x1mfz",
  "venue": "HAL",
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}