Ununfoldable polyhedra with convex faces

Computational Geometry: Theory and Applications

Volumn 24, Issue 2, 2003, Pages 51-62

  Bern, Marshall ^a   Demaine, Erik D ^b   Eppstein, David ^c   Kuo, Eric ^d   Mantler, Andrea ^e   Snoeyink, Jack ^e,f  

^a PALO ALTO RESEARCH CENTER   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^f Brooks Computer Science Building   (United States)

Author keywords

Discrete geometry; Nets; Unfolding polyhedra

Indexed keywords

EID: 84867951846     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-7721(02)00091-3     Document Type: Article

References (27)

1. P.K. Agarwal, B. Aronov, J. O'Rourke, and C.A. Schevon Star unfolding of a polytope with applications SIAM J. Comput. 26 6 1997 1689 1713
2. B. Aronov, and J. O'Rourke Nonoverlap of the star unfolding Discrete Comput. Geom. 8 3 1992 219 250
3. M. Bern, E.D. Demaine, D. Eppstein, and E. Kuo Ununfoldable polyhedra Proceedings of the 11th Canadian Conference on Computational Geometry, Vancouver, Canada 1999 http://www.cs.ubc.ca/conferences/CCCG/elec-proc/fp38.ps. gz. Also Technical Report CS-99-04, Department of Computer Science, University of Waterloo, August 1999
4. T. Biedl, E. Demaine, M. Demaine, A. Lubiw, M. Overmars, J. O'Rourke, S. Robbins, and S. Whitesides Unfolding some classes of orthogonal polyhedra Proceedings of the 10th Canadian Conference on Computational Geometry, Montréal, Canada 1998 http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98- biedl-unfolding.ps.gz
5. H.T. Croft, K.J. Falconer, and R.K. Guy Unsolved Problems in Geometry 1991 Springer-Verlag 73 76
6. P.R. Cromwell Polyhedra 1997 Cambridge University Press
7. H.M. Cundy, and A.P. Rollett Polyhedra Mathematical Models 2nd edition 1961 Oxford University Press Chapter 3, pp. 76-160
8. E. Demaine, M. Demaine, A. Lubiw, J. O'Rourke, Examples, counterexamples, and enumeration results for foldings and unfoldings between polygons and polytopes, Technical Report 069, Smith College, Northampton, MA, July 2000. http://www.arXiv.org/abs/cs.CG/0007019
9. E.D. Demaine, M.L. Demaine, A. Lubiw, and J. O'Rourke Enumerating foldings and unfoldings between polygons and polytopes Proceedings of the Japan Conference on Discrete and Computational Geometry, Tokyo, Japan 2000 http://www.arXiv.org/abs/cs.CG/0107024
10. E.D. Demaine, D. Eppstein, J. Erickson, G.W. Hart, J. O'Rourke, Vertex-unfoldings of simplicial polyhedra, July 2001, arXiv:cs.CG/0107023. http://www.arXiv.org/abs/cs.CG/0107023
11. A. Dürer The Painter's Manual: A Manual of Measurement of Lines, Areas, and Solids by Means of Compass and Ruler Assembled by Albrecht Dürer for the Use of All Lovers of Art with Appropriate Illustrations Arranged to be Printed in the Year MDXXV 1977 Abaris Books New York English translation of: Unterweysung der Messung mit dem Zirkel un Richtscheyt in Linien Ebnen uhnd Gantzen Corporen, 1525
12. K. Fukuda, Strange unfoldings of convex polytopes, June 1997. http://www.ifor.math.ethz.ch/staff/fukuda/unfold-home/unfold-open.html
13. B. Grünbaum Convex Polytopes 1967 Interscience New York
14. S.K. Gupta, D.A. Bourne, K.H. Kim, and S.S. Krishnan Automated process planning for sheet metal bending operations J. Manufacturing Systems 17 5 1998 338 360
15. B. Hayes, Pleasures of plication, American Scientist, November-December 1995. See also http://www.cs.colorado.edu/~eisenbea/hypergami/ for information on HyperGami
16. M. Henk, J. Richter-Gebert, and G.M. Ziegler Basic properties of convex polytopes J.E. Goodman, J. O'Rourke, Handbook of Discrete and Computational Geometry 1997 CRC Press Boca Raton Chapter 13, pp. 243-270
17. Lundstrom Design, Touch-3d, July 1998. http://www.algonet.se/~ludesign/
18. J.S.B. Mitchell, D.M. Mount, and C.H. Papadimitriou The discrete geodesic problem SIAM J. Comput. 16 4 1987 647 668
19. M. Namiki, K. Fukuda, Unfolding 3-dimensional convex polytopes: A package for Mathematica 1.2 or 2.0, Version 1.0, September 1994. ftp://ftp.ifor.math. ethz.ch/pub/fukuda/mathematica/UnfoldPolytope.tar.Z
20. J. O'Rourke Folding and unfolding in computational geometry Revised Papers from the Japan Conference on Discrete and Computational Geometry, Tokyo, Japan Lecture Notes in Computer Science 1763 1998 258 266
21. C. Schevon, Unfolding polyhedra. sci.math Usenet article, February 1987. See http://www.ics.uci.edu/~eppstein/gina/unfold.html
22. C. Schevon, Algorithms for geodesics on polytopes, PhD Thesis, Johns Hopkins University, 1989
23. M. Sharir, and A. Schorr On shortest paths in polyhedral spaces SIAM J. Comput. 15 1 1986 193 215
24. G.C. Shephard Convex polytopes with convex nets Math. Proc. Cambridge Philos. Soc. 78 1975 389 403
25. E. Steinitz, and H. Rademacher Vorlesungen über die Theorie der Polyeder 1934 Springer-Verlag Berlin Reprinted 1976
26. C.-H. Wang, Manufacturability-driven decomposition of sheet metal, PhD Thesis, Carnegie Mellon University, Robotics Institute, Technical Report CMU-RI-TR-97-35, September 1997
27. M.J. Wenninger Polyhedron Models 1971 Cambridge University Press