{
  "abstract": "The regular ideal right-angled 24-cell has volume $4 π^2/3$ and is the unique minimum-volume entirely ideal right-angled hyperbolic four-polytope. We prove that the next distinct volume is $8 π^2/3$ and that its unique equality case is the reflection double of the 24-cell across one octahedral facet. We also show that an entirely ideal right-angled four-polytope whose facets are regular ideal octahedra or their doubles across triangular faces decomposes into a chain of regular 24-cells, with opposite cutting facets in each intermediate cell.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00118",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Kolpakov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fxyedzc0tt9qa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00118",
  "fulltext_url": null,
  "id": "fxyedzc0tt9qa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00118",
  "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.GT"
    ],
    [
      "arxiv",
      "math.MG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00118",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fxyedzc0tt9qa.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00118",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00118"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the second smallest ideal right-angled hyperbolic four-polytope",
  "title_text": "On the second smallest ideal right-angled hyperbolic four-polytope",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fxyedzc0tt9qa",
  "venue": "arXiv",
  "versions": []
}