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How do I test whether a given undirected graph is the 1-skeleton of a polytope? How can I tell the dimension of a given 1-skeleton?

Given a graph $G$, a realization of $G$ as a polytope is a convex polytope $P\subseteq \Bbb R^n$ with $G$ as its 1-skeleton. A realization $P\subseteq \Bbb R^n$ is said to realize the symmetries of $...