{
  "abstract": "We study finite-volume convex hyperbolic $4$-polytopes whose dihedral angles are all equal to a fixed strictly acute angle $α$. Put $α_0=\\arccos(1/3)$ and $α_1=\\arccos(1/4)$. We first show that the class is empty for $α<α_0$. For $α_0\\leqα<α_1$, the unique polytope of minimum volume is the regular hyperbolic $4$-simplex with dihedral angle $α$. As $α$ increases to $α_1$, this simplex degenerates to a Euclidean one and no hyperbolic simplex exists at $α_1$. For $α_1\\leqα<π/2$, the unique minimum is the regular equiangular hyperbolic $4$-cube. The proof combines the hyperbolic Gram--Euler relation with the Davis--Okun theorem on the Charney--Davis inequality for flag triangulations of the $3$-sphere. The geometric step is a missing-face argument showing that the boundary of the dual of every nonsimplex in the class is flag.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04258",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrey Egorov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7r6wpyb7xcy82.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04258",
  "fulltext_url": null,
  "id": "7r6wpyb7xcy82",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04258",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7211911601",
  "pdf_url": "https://arxiv.org/pdf/2609.04258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7r6wpyb7xcy82.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Minimal-Volume Equiangular Hyperbolic $4$-Polytopes",
  "title_text": "Minimal-Volume Equiangular Hyperbolic $4$-Polytopes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/7r6wpyb7xcy82",
  "venue": "arXiv",
  "versions": []
}