{
  "id": "2309.13177",
  "version": "v1",
  "published": "2023-09-22T20:47:28.000Z",
  "updated": "2023-09-22T20:47:28.000Z",
  "title": "Mean distance in polyhedra",
  "authors": [
    "Dominik Beck"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Given any polyhedron from which we select two random points uniformly and independently, we show that all the moments of the distance between those points can be always written in terms of elementary functions. As an illustration, the mean distance is found in the exact form for all Platonic solids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-22T20:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "52A22",
      "G.3"
    ],
    "keywords": [
      "mean distance",
      "polyhedron",
      "random points",
      "elementary functions",
      "exact form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}