{
  "abstract": "We present a fixed nondegenerate tetrahedron with a nested largest-dihedral-anglebisection branch that collapses onto a unit edge. The selected dihedral angles to bisect are uniquely largest ones at every bisection step. Some face angles of the branch elements tend to zero, the corresponding diameter-to-inradius ratio diverges, and the diameters of the elements produced do not tend to zero, although every dihedral angle stays uniformly away from both 0 and π and all face and dihedral angles satisfy a uniform maximum-angle bound. The proof is based on an exact invariant-range argument. This example shows that the largest-dihedral-angle bisection algorithm can produce degenerating tetrahedral partitions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18788",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergey Korotov"
    },
    {
      "name": "Jérôme Michaud"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ehh07w70mpfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18788",
  "fulltext_url": null,
  "id": "4ehh07w70mpfd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18788",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7213524662",
  "pdf_url": "https://arxiv.org/pdf/2609.18788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ehh07w70mpfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18788"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Largest-dihedral-angle bisection algorithm does not preserve mesh regularity for tetrahedral partitions",
  "title_text": "Largest-dihedral-angle bisection algorithm does not preserve mesh regularity for tetrahedral partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/4ehh07w70mpfd",
  "venue": "arXiv",
  "versions": []
}