Continuous Flattening of the 2-Dimensional Skeleton of the Square Faces in a Hypercube

The surface of a 3-dimensional cube can be continuously flattened onto any of its faces, by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. Let C_n be an n -dimensional cube with n ≥ 4 , and S be the set of its 2-dimensional faces, i.e., the 2-dimensional skeleton of the square faces in C_n . We show that S can be continuously flattened onto any face F of S , such that the faces of S that are parallel to F , do not have any crease, that is, they are rigid during the motion.