Polytopality of Maniplexes
Jorge Garza-Vargas, Isabel Hubard

TL;DR
This paper characterizes when a maniplex's associated poset is an abstract polytope and establishes conditions under which the maniplex is isomorphic to a polytope's flag graph.
Contribution
It provides necessary and sufficient graph-theoretic conditions for a maniplex to correspond to an abstract polytope and shows the isomorphism between such maniplexes and polytope flag graphs.
Findings
Characterization of when a maniplex's associated poset is an abstract polytope.
Conditions under which a maniplex is isomorphic to a polytope's flag graph.
Establishment of a correspondence between maniplexes and abstract polytopes.
Abstract
Given an abstract polytope , its flag graph is the edge-coloured graph whose vertices are the flags of and the -edges correspond to -adjacent flags. Flag graphs of polytopes are maniplexes. On the other hand, given a maniplex , on can define a poset 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 in order for to be an abstract polytope. Moreover, in such case, we show that is isomorphic to the flag graph of . This in turn gives necessary and sufficient conditions for a maniplex to be (isomorphic to) the flag graph of a polytope.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
