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Is the space of Euclidean polyhedra with a fixed $1$-skeleton connected?

Let $\mathcal{A}_\Gamma$ be the space of convex (non-degenerate) Euclidean polyhedra with $1$-skeleton a certain polyhedral graph $\Gamma$. … It is a well known fact (for example in Proposition 17 of Deformations of hyperbolic convex polyhedra and cone-$3$-manifolds by Montcouquiol) that $\mathcal{A}_\Gamma$ is a manifold. …
Giulio Belletti's user avatar