Video Description: The Metamorphosis of the Cube is a video envisioned and created by Erik Demaine, Martin Demaine, Anna Lubiw, Joseph O'Rourke, and Irena Pashchenko.

For more information, see the authors' paper “Enumerating Foldings and Unfolding between Polygons and Polytopes”
 
A Cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

A Polygon is a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line.

Polytope means, first, the generalization to any dimension of polygon in two dimensions, polyhedron in three dimensions, and polychoron in four dimensions.
The Platonic solids, or regular polytopes in three dimensions, were a major focus of study of ancient Greek mathematicians (most notably Euclid's Elements), probably because of their intrinsic aesthetic qualities. In modern times, polytopes and related concepts have found important applications in computer graphics, optimization, search engines and numerous other fields. Source: Wikipedia.