{
  "abstract": "We construct a compact set of diameter $1$ in $\\mathbb{R}^5$ which cannot be covered by six Euclidean balls of diameter $1$. Its convex hull is a full-dimensional convex body satisfying the same property. Moreover, a finite subset of diameter $1$ cannot be covered by six closed balls even when their radius is increased to $0.50001$. The compact set is the quadratic image of the unit sphere in the space of symmetric $3\\times3$ matrices of trace zero. A hypothetical cover leads to twelve spherical ellipses covering ${\\mathbb S}^2$ and arranged in six antipodal pairs. Using Euler's formula, we replace them by twelve pentagonal regions contained in the ellipses. An area estimate then gives a contradiction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08198",
  "author_total": 4,
  "authors": [
    {
      "name": "A. Arman"
    },
    {
      "name": "A. Bondarenko"
    },
    {
      "name": "A. Prymak"
    },
    {
      "name": "D. Radchenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vk41qfk2vz16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08198",
  "fulltext_url": null,
  "id": "0vk41qfk2vz16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08198",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vk41qfk2vz16.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A diameter-one set in $\\mathbb{R}^5$ that cannot be covered by six diameter-one balls",
  "title_text": "A diameter-one set in ℝ^5 that cannot be covered by six diameter-one balls",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:49Z",
  "url": "https://research.draconitic.com/paper/0vk41qfk2vz16",
  "venue": "arXiv",
  "versions": []
}