{
  "id": "1604.00580",
  "version": "v1",
  "published": "2016-04-03T01:18:28.000Z",
  "updated": "2016-04-03T01:18:28.000Z",
  "title": "Rectifications of Convex Polyhedra",
  "authors": [
    "Samuel Reid"
  ],
  "comment": "7 pages, 3 figures",
  "categories": [
    "math.MG"
  ],
  "abstract": "A convex polyhedron, that is, a compact convex subset of $\\mathbb{R}^3$ which is the intersection of finitely many closed half-spaces, can be rectified by taking the convex hull of the midpoints of the edges of the polyhedron. We derive expressions for the side lengths and areas of rectifications of regular polygons in plane, and use these results to compute surface areas and volumes of various convex polyhedra. We introduce rectification sequences and show that there are exactly two disjoint pure rectification sequences generated by the platonic solids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-03T01:18:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A15"
    ],
    "keywords": [
      "convex polyhedron",
      "disjoint pure rectification sequences",
      "compact convex subset",
      "convex hull",
      "side lengths"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}