{
  "id": "1604.01164",
  "version": "v1",
  "published": "2016-04-05T08:12:04.000Z",
  "updated": "2016-04-05T08:12:04.000Z",
  "title": "Polytopality of Maniplexes",
  "authors": [
    "Jorge Garza-Vargas",
    "Isabel Hubard"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given an abstract polytope $\\cal P$, its flag graph is the edge-coloured graph whose vertices are the flags of $\\cal P$ and the $i$-edges correspond to $i$-adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, given a maniplex $\\cal M$, on can define a poset $\\cal P_M$ by means of the non empty intersection of its faces. In this paper we give necessary and sufficient conditions (in terms of graphs) on a maniplex $\\cal M$ in order for $\\cal P_M$ to be an abstract polytope. Moreover, in such case, we show that $\\cal M$ is isomorphic to the flag graph of $\\cal P_M$. This in turn gives necessary and sufficient conditions for a maniplex to be (isomorphic to) the flag graph of a polytope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-05T08:12:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "flag graph",
      "polytopality",
      "abstract polytope",
      "sufficient conditions",
      "non empty intersection"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}