{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, a **matroid polytope**, also called a **matroid basis polytope** (or **basis matroid polytope**) to distinguish it from other polytopes derived from a matroid, is a polytope constructed via the bases of a matroid. Given a matroid $M$, the matroid polytope $P_M$ is the [[convex hull|0FQSDC2EQ2]] of the indicator vectors of the bases of $M$.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "6HXVVMHMWJ"
    ],
    "kind": "concept",
    "name": "Matroid polytope",
    "same_as": {
      "wikidata": "Q6787907",
      "wikipedia": "Matroid polytope"
    },
    "sources": [
      {
        "locator": "Matroid polytope",
        "mention": "wikipedia://en/38726681",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:38726681@r1313002274"
      }
    ],
    "tag": "38ENJ7JHPJ"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/38ENJ7JHPJ/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/38ENJ7JHPJ.md",
  "msc": null,
  "name": "Matroid polytope",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/38E/38ENJ7JHPJ.md",
  "status": null,
  "tag": "38ENJ7JHPJ",
  "uri": "m2://38ENJ7JHPJ",
  "url": "https://math2.tamnd.com/wiki/matroid-polytope/",
  "writing": {
    "tag": "38ENJ7JHPJ",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}