Continuous flattening of the 2-skeletons in regular simplexes and cross-polytopes

摘要

We previously showed one can continuously flatten the surface of a regular tetrahedron onto any of its faces without stretching and cutting. This is accomplished by moving creases to change the shapes of some faces successively, following Sabitov’s volume preserving theorem. We extend this result to higher dimensional regular simplexes and cross-polytopes by considering the 2-dimensional skeleton of a polytope corresponding to the surface of a three dimensional polyhedron.