{
  "aliases": [
    "full-flag-conjecture",
    "kalais-3d-conjecture"
  ],
  "backlinks": null,
  "body": "\n## Statement\n\nIn geometry, more specifically in polytope theory, **Kalai's 3\u003csup\u003e*d*\u003c/sup\u003e conjecture** is a conjecture on the polyhedral combinatorics of centrally symmetric polytopes, made by Gil Kalai in 1989. It states that every *d*-dimensional centrally symmetric polytope has at least 3\u003csup\u003e*d*\u003c/sup\u003e nonempty faces (including the polytope itself as a face but not including the [[empty set|0ECVK59Y03]]).\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "full-flag-conjecture",
      "kalais-3d-conjecture"
    ],
    "inventory": [
      "S87DCMV9X3"
    ],
    "kind": "conjecture",
    "name": "Kalai's 3^d conjecture",
    "same_as": {
      "wikidata": "Q17077841",
      "wikipedia": "Kalai's 3^d conjecture"
    },
    "sources": [
      {
        "locator": "Kalai's 3^d conjecture",
        "mention": "wikipedia://en/39408412",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:39408412@r1364111300"
      }
    ],
    "tag": "5CRY9ZK4Y2"
  },
  "kind": "conjecture",
  "link": "https://math2.tamnd.com/node/5CRY9ZK4Y2/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/5CRY9ZK4Y2.md",
  "msc": null,
  "name": "Kalai's 3^d conjecture",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/5CR/5CRY9ZK4Y2.md",
  "status": null,
  "tag": "5CRY9ZK4Y2",
  "uri": "m2://5CRY9ZK4Y2",
  "url": "https://math2.tamnd.com/wiki/kalais-3-d-conjecture/",
  "writing": {
    "tag": "5CRY9ZK4Y2",
    "kind": "conjecture",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "have": 0,
        "want": 1
      }
    ]
  }
}