{
  "id": "2408.09911",
  "version": "v1",
  "published": "2024-08-19T11:36:01.000Z",
  "updated": "2024-08-19T11:36:01.000Z",
  "title": "On $m$-point homogeneous polyhedra in $3$-dimensional Euclidean space",
  "authors": [
    "V. N. Berestovskii",
    "Yu. G. Nikonorov"
  ],
  "comment": "34 pages, 22 figures, comments are welcome!",
  "categories": [
    "math.MG"
  ],
  "abstract": "This paper is devoted to the study of the $m$-point homogeneity property for the vertex sets of polytopes in Euclidean spaces. In particular, we present the classifications of $2$-point and $3$-point homogeneous polyhedra in $\\mathbb{R}^3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-19T11:36:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54E35",
      "52B15",
      "20B05"
    ],
    "keywords": [
      "point homogeneous polyhedra",
      "dimensional euclidean space",
      "point homogeneity property",
      "vertex sets",
      "classifications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}