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The Metamorphosis of the Cube is a video envisioned and created by Erik Demaine, Martin Demaine, Anna Lubiw, Joseph O'Rourke, and Irena Pashchenko. It appears in a refereed video collection, the 8th Annual Video Review of Computational Geometry, associated with the 15th Annual ACM Symposium on Computational Geometry (SoCG'99).
The video is based on work studying foldings of polygons into convex polyhedra, and the reverse, unfoldings of convex polyhedra into polygons. For more information, see the paper “Enumerating Foldings and Unfolding between Polygons and Polytopes”, the longer technical report “Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes”, and Anna and Joe's original technical report, “When can a polygon fold to a polytope?”.