**Reference**:- Zachary Abel, Robert Connelly, Erik D. Demaine, Martin Demaine, Thomas Hull, Anna Lubiw, and Tomohiro Tachi, “Rigid Flattening of Polyhedra with Slits”, in
*Origami*, volume 1, Tokyo, Japan, August 10–13, 2014, pages 109–118, American Mathematical Society.^{6}: Proceedings of the 6th International Meeting on Origami in Science, Mathematics and Education (OSME 2014) **Abstract**:- Cauchy showed that if the faces of a convex polyhedron are rigid then the whole polyhedron is rigid. Connelly showed that this is true even if finitely many extra creases are added. However, cutting the surface of the polyhedron destroys rigidity and may even allow the polyhedron to be flattened. We initiate the study of how much the surface of a convex polyhedron must be cut to allow continuous flattening with rigid faces. We show that a regular tetrahedron with side lengths 1 can be continuously flattened with rigid faces after cutting a slit of length .046 and adding a few extra creases.
**Availability**:- The paper is available in PDF (1279k).
- See information on file formats.
- [Google Scholar search]
**Related papers**:- TetraFlattening_OSME2014 (Rigid Flattening of Polyhedra with Slits)

See also other papers by Erik Demaine.

Last updated May 4, 2022 by Erik Demaine.