{
  "abstract": "Hitomezashi is a particular style of sashiko stitching characterized by crossing lines of stitches. Certain hitomezashi designs can be encoded with two binary strings and have been the subject of a wide-array of mathematical research. Dubbed generalized hitomezashi patterns (GHPs) by Sen & Martinez, these designs are reversible and can be 'self-dual.' We investigate the possible 'dual-' or 'flip-symmetries' in GHPs; the inclusion of these symmetries is equivalent to considering two-colour symmetry groups. Following the work of Sen & Martinez, who found the wallpaper symmetry groups that are compatible with GHPs, this paper investigates the possible two-colour symmetries compatible with GHPs. We prove that there are four possible rosette two-colour symmetry types, completely describe the properties on binary strings that create these symmetries, and prove that exactly 17 of the 46 two-colour wallpaper groups are compatible with GHPs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27542",
  "author_total": 1,
  "authors": [
    {
      "name": "Megan A. Martinez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24enzyz09y2k7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27542",
  "fulltext_url": null,
  "id": "24enzyz09y2k7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27542",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7204768003",
  "pdf_url": "https://arxiv.org/pdf/2608.27542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24enzyz09y2k7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Mathematics and Applications",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Whole New Side: The Duality Symmetries of Hitomezashi",
  "title_text": "A Whole New Side: The Duality Symmetries of Hitomezashi",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/24enzyz09y2k7",
  "venue": "arXiv",
  "versions": []
}