{
  "abstract": "Can a LEGO model built from many kinds of rectangular bricks be rebuilt using only the familiar $2\\times4$ brick? Enlarging every dimension by four makes the pieces fit, but they must also connect. We give a four-layer arrangement that joins every finite face-connected union of lattice cubes, using eight upright bricks per source cube, and show that no smaller universal enlargement works. A second question has an unexpected answer: if connectivity is set aside, the minimum integer scale is always $1$, $2$, or $4$, never $3$. The missing value follows from a checkerboard argument applied separately inside each enlarged cell.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09205",
  "author_total": 1,
  "authors": [
    {
      "name": "Joshua S. Gans"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9p7vapt6me0b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09205",
  "fulltext_url": null,
  "id": "c9p7vapt6me0b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09205",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212135361",
  "pdf_url": "https://arxiv.org/pdf/2609.09205",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9p7vapt6me0b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09205",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09205"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Fourfold Is Enough: Connected LEGO Models from One Brick Type",
  "title_text": "Fourfold Is Enough: Connected LEGO Models from One Brick Type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/c9p7vapt6me0b",
  "venue": "arXiv",
  "versions": []
}