{
  "abstract": "Recently, a new record kissing arrangement of $841$ points in $\\mathbb R^{12}$ was obtained numerically by optimization (Takhanov-Assylbekov-Yun, 2026). The configuration was released as a coordinate file, without a mathematical description of its structure. The purpose of this paper is to provide such a description. The key observation is that the geometry becomes transparent once we regard $\\mathbb R^{12}\\cong \\mathbb H^3$ as the Cartesian product of three copies of the quaternion algebra. We first introduce a new $840$-point kissing arrangement with a certain quaternionic structure. It consists of three mutually orthogonal regular $24$-cells, supported on the three quaternionic coordinate factors $\\mathbb H\\times\\{0\\}\\times\\{0\\}$, $\\{0\\}\\times\\mathbb H\\times\\{0\\}$, $\\{0\\}\\times\\{0\\}\\times\\mathbb H$, together with two $384$-point families obtained by lifting affine sets of the form $$\\{(u,v,w)\\in (\\mathbb F_2^2)^3\\mid u+v+w=η\\},$$ to quaternionic triples (whose components belong to the binary octahedral group $2O$) and then applying suitable component-wise rotations and weightings. A characteristic feature of this construction is a pronounced asymmetry among the three quaternionic factors. For the $816$ vectors obtained after removing the third $24$-cell, most of the squared norm is concentrated in the first two quaternionic coordinates, while the third coordinate carries systematically less mass. Thus, the third four-dimensional factor contains more available space than the first two. We then show that this $840$-point configuration provides a natural structural model for the numerical $841$-point record. Finally, we introduce a notion of the general quaternionic construction in dimensions divisible by $4$, and check that record kissing arrangements in ${\\mathbb R}^{4k}$, $k\\leq 5$, admit a quaternionic construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09179",
  "author_total": 1,
  "authors": [
    {
      "name": "Rustem Takhanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9agtrr1mc1rj8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09179",
  "fulltext_url": null,
  "id": "9agtrr1mc1rj8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09179",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212161083",
  "pdf_url": "https://arxiv.org/pdf/2609.09179",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9agtrr1mc1rj8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.09179",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09179"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A quaternionic construction behind $841$-point kissing arrangement in ${\\mathbb R}^{12}$",
  "title_text": "A quaternionic construction behind $841$-point kissing arrangement in ℝ^12",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/9agtrr1mc1rj8",
  "venue": "arXiv",
  "versions": []
}