{
  "abstract": "We study \\emph{prismatical} polytopes, those all of whose facets are combinatorially isomorphic to the simplicial prism $Δ^{d-2}\\timesΔ^1$. In dimension three these are exactly the cubical polytopes, so the class sits naturally between simplicial and cubical polytopes. In dimension four, $Δ^2\\timesΔ^2$ is the simplest prismatical polytope and we can construct infinitely many by using connected sums. By fibreing a triangle over a triangulated polygon we construct infinitely many connected-sum-prime prismatical $4$-polytopes. Finally, we show that there are no prismatical $d$-polytopes for $d\\ge5$, answering a question of Perles and Shephard.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32035",
  "author_total": 3,
  "authors": [
    {
      "name": "Federico Castillo"
    },
    {
      "name": "Guillermo Piñeda-Villavicencio"
    },
    {
      "name": "José Alejandro Samper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bb8thbwt0qapw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32035",
  "fulltext_url": null,
  "id": "bb8thbwt0qapw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32035",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223692131",
  "pdf_url": "https://arxiv.org/pdf/2610.32035",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bb8thbwt0qapw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32035",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32035"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Equifacetted polytopes whose facets are products of simplices: The simplicial prism case",
  "title_text": "Equifacetted polytopes whose facets are products of simplices: The simplicial prism case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/bb8thbwt0qapw",
  "venue": "arXiv",
  "versions": []
}