Ezra Miller
Most of us as children saw those paper or cardboard cutouts, which we could call ``foldouts'', whose edges glue to form (boundaries of) 3-dimensional convex polyhedra. Just how did anyone figure out how to make them? Given a 3-dimensional convex polyhedron, does there always exist a foldout in the plane? What about higher dimensions? These questions have surprising answers, depending on the precise meaning of ``foldout''.
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