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- W4301317022 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." @default.
- W4301317022 created "2022-10-05" @default.
- W4301317022 creator A5039876691 @default.
- W4301317022 creator A5090566063 @default.
- W4301317022 date "2016-04-05" @default.
- W4301317022 modified "2023-09-27" @default.
- W4301317022 title "Polytopality of Maniplexes" @default.
- W4301317022 doi "https://doi.org/10.48550/arxiv.1604.01164" @default.
- W4301317022 hasPublicationYear "2016" @default.
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