{
  "abstract": "For every $n\\geq2$, we consider a Gaussian zonoid of revolution $Z_n$ arising from works of Vitale and Mathis. We prove that $Z_n^*$ is also a zonoid and compute the Banach--Mazur distance from $Z_n$ to the Euclidean ball. This distance is independent of the dimension and is approximately $1.10$. Consequently, the supremal Banach--Mazur distance among zonoids whose polars are zonoids does not converge to $1$. The construction also produces a separable real Banach space $X$, not isometric to a Hilbert space, such that both $X$ and $X^*$ embed linearly isometrically into $L_1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10852",
  "author_total": 2,
  "authors": [
    {
      "name": "Dmitry Ryabogin"
    },
    {
      "name": "Artem Zvavitch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j20yf499z6g7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10852",
  "fulltext_url": null,
  "id": "4j20yf499z6g7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10852",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7212316245",
  "pdf_url": "https://arxiv.org/pdf/2609.10852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j20yf499z6g7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Zonoids whose polars are zonoids: the Banach--Mazur distance need not tend to one",
  "title_text": "Zonoids whose polars are zonoids: the Banach--Mazur distance need not tend to one",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/4j20yf499z6g7",
  "venue": "arXiv",
  "versions": []
}