Geometric Folding Algorithms:
Linkages, Origami, Polyhedra

by Erik D. Demaine and Joseph O'Rourke

Closed Open Problems
(and Advances on Open Problems)

Last Update:

The book contains many open problems (see the Index under Open Problems, p. 468). Inevitably, some will be resolved as time passes and before we can release a Second Edition. Here we will maintain a list of those Open Problems in the book which either have been closed, or on which there has been reportable progress of which investigators should be aware.

  1. Alexander I. Bobenko and Ivan Izmestiev. "Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes," Annales de l'institut Fourier, 58 No. 2 (2008), p. 447-505.
  2. Daniel Kane, Gregory N. Price, Erik D. Demaine, "A Pseudopolynomial Algorithm for Alexandrov's Theorem," arXiv:0812.5030v1 [cs.CG], 2008.
  3. Joseph O'Rourke, "Computational Geometry Column 49," SIGACT News, Vol. 38, No. 2, Issue 143, June 2007, pp. 55-59.
  4. Gregory N. Price and Erik D. Demaine, "Generalized D-forms have no spurious creases, Discrete & Comptutational Geometry, 43(1) 179-186.
  5. Yu. D. Burago and V. A. Zalgaller. "Isometric piecewise linear immersions of two-dimensional manifolds with polyhedral metrics into R3." St. Petersburg Math. J., 7(3):369--385, 1996.
  6. J. O'Rourke, "On Folding a Polygon to a Polyhedron," arXiv:1007.3181v1 [cs.CG], July 2010.
  7. Jin-ichi Itoh, Chie Nara, Costin Vilcu, "Continuous flattening of convex polyhedra," XIV Spanish Meeting on Computational Geometry, 2011, Centre de Recerca Matematica Documents Vol. 8, pp. 95-98.
  8. J. O'Rourke, "On Flat Polyhedra deriving from Alexandrov's Theorem," 1007.2016v1 [cs.CG], July 2010.
  9. J. O'Rourke, "Band Unfoldings and Prismatoids: A Counterexample." Smith Computer Science Technical Report 087, Oct. 2007. arXiv:0710.0811v2 [cs.CG].