Abstract. We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a continuous folding process for polyhedra.

Abstract. We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a continuous folding process for polyhedra.

Nov 3, 2010 · We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a continuous folding process for polyhedra.

Apr 26, 2021 · We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding ...

We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and avoiding crossings.

For the five Platonic polyhedra there are continuous flat folding processes onto their original faces. Figure 1 shows how to continuously flatten the cube and ...

We prove that each Platonic polyhedron P can be folded into a flat multilayered face of P by a continuous folding process for polyhedra.

May 22, 2021 · Abstract:We prove that any finite polyhedral manifold in 3D can be continuously flattened into 2D while preserving intrinsic distances and ...

For any Platonic solid, there exists a continuous flat- tening motion whose area of moving creases is arbitrarily small. Proof. A cube, a regular tetrahedron ...

It is an open problem of E. Demaine et al., that every flat folded state of a polyhedron can be reached by a continuous folding process. Here we prove that ...