{
  "abstract": "The Pythagoras tree of A. E. Bosman (1942) is drawn with squares in the plane and, in the three-dimensional versions we know of, with cubes. This article documents a tree built instead from regular dodecahedra: each dodecahedron carries five smaller copies, one on each edge of a single pentagonal \"crown\" face, scaled by $g \\approx 0.4346$ and twisted by $45^\\circ$ about the edge. The construction first existed only as a pair of rendered images and two undocumented C++ programs. We recover its exact parameters from the original Blender scene, reformulate it as an iterated function system with condensation, and prove with a short computer-assisted argument that it never collides with itself: two of its dodecahedra overlap only when one is the parent of the other. A Pythagorean identity for the six face axes of the dodecahedron singles out the scale $1/\\sqrt{5}$ and the twist $\\arccos(1/\\sqrt{5})$. With these values each child rests flat against a face of its parent, the five children together have exactly the parent's surface area, and the crown of the tree is a fractal of Hausdorff dimension exactly 2. Finally we ask whether the tree can grow on all twelve faces at once. A parity argument shows that at the artwork's proportions it cannot, but smaller scale factors admit certified clash-free all-faces trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33975",
  "author_total": 1,
  "authors": [
    {
      "name": "Miguel Esteban Pérez Ibarra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5px3vdeqypm99.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33975",
  "fulltext_url": null,
  "id": "5px3vdeqypm99",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33975",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.HO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7224001250",
  "pdf_url": "https://arxiv.org/pdf/2610.33975",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5px3vdeqypm99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33975",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33975"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Pythagoras Tree Grown from a Dodecahedron",
  "title_text": "A Pythagoras Tree Grown from a Dodecahedron",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/5px3vdeqypm99",
  "venue": "arXiv",
  "versions": []
}