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arXiv · 1604.01164

Polytopality of Maniplexes

Jorge Garza-Vargas·Isabel Hubard
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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.

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Jorge Garza-Vargas, Isabel Hubard. 2016-04-05. Polytopality of Maniplexes. https://arxiv.org/abs/1604.01164

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