Edge unfoldings of platonic solids never overlap

Proceedings of the 23rd Annual Canadian Conference on Computational Geometry, CCCG 2011

Volumn , Issue , 2011, Pages

  Horiyama, Takashi ^a   Shoji, Wataru ^a  

^a SAITAMA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ARCHIMEDEAN SOLIDS; NONOVERLAPPING; PLATONIC SOLIDS; SIMPLE POLYGON; UNFOLDINGS;

COMPUTATIONAL GEOMETRY;

EID: 84882967483     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. S. B. Akers, Binary decision diagrams, IEEE Trans. Com., C-27:509-516, 1978.
2. J. Akiyama, Tile-Makers and Semi-Tile-Makers, Math. Assoc. America, 114:602-609, 2007.
3. B. Aronov and J. O'Rourke, Nonoverlap of the star unfolding, Disc. Comp. Geom., 8:219-250, 1992.
4. T. Biedl, E. D. Demaine, M. L. Demaine, A. Lubiw, J. O'Rourke, M. Overmars, S. Robbins, and S. Whitesides, Unfolding some classes of orthogonal polyhedra, Proc. CCCG, 70-71, 1998.
5. E. Boros, T. Ibaraki, and K. Makino, Monotone extensions of Boolean data sets, Proc. ALT, LNCS 1316, 161-175, 1997.
6. S. Bouzette, and F. Vandamme, The regular Dodecahedron and Icosahedron unfold in 43380 ways, Unpublished manuscript.
7. R. E. Bryant, Graph-based algorithms for Boolean function manipulation, IEEE Trans. Com., C-35: 677-691, 1986.
8. J. R. Burch, E. M. Clarke, K. L. McMillan, and D. L. Dill, Sequential circuit verification using symbolic model checking, Proc. DAC, 46-51, 1990.
9. H. T. Croft, K. J. Falconer, and R. K. Guy, Unsolved Problems in Geometry, Springer-Verlag, Reissue edition, 1995.
10. E. D. Demaine and J. O'Rourke. Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press, 2007.
11. A. Dürer, Unterweysung der Messung mit dem Zirkel un Richtscheyt in Linien Ebnen uhnd Gantzen Corporen, 1525.
12. B. Grünbaum, Are your polyhedra the same as my polyhedra?, In B. Aronov, et al. (eds.), Discrete and Computational Geometry: The Goodman- Pollack Festschrift, 461-488, Springer, 2003.
13. C. Hippenmeyer, Die Anzahl der inkongruenten ebenen Netze eines regulären Ikosaeders, Elem. Math., 34:61-63, 1979.
14. T. Horiyama and T. Ibaraki, Reasoning with ordered binary decision diagrams, Proc. ISAAC, LNCS 1969, 120-131, 2000.
15. M. Jeger, Über die Anzahl der inkongruenten ebenen Netze des Würfels und des regulären Oktaeders, Elemente der Mathematik, 30:73-83, 1975.
16. D. E. Knuth, The art of computer programming, vol. 4, fascicle 1, Bitwise tricks & techniques, Binary decision diagrams, Addison-Wesley, 2009.
17. S. Minato, "Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems, " Proc. DAC, 272-277, 1993.
18. S. Minato, Arithmetic Boolean expression manipulator using BDDs, Formal methods in system design, 10:221-242, Kluwer Academic, 1997.
19. S. Minato and H. Arimura, Frequent Pattern Mining and Knowledge Indexing Basedon Zero- Suppressed BDDs, Proc. KDID, 152-169, 2006.
20. J. Mitani and R. Uehara, Polygons Folding to Plural Incongruent Orthogonal Boxes, Proc. CCCG, 31-34, 2008.
21. D. M. Mount, On folding shortest paths on convex polyhedra, Technical Report 1495, Department of Computer Science, University of Maryland, 1985.
22. M. Namiki and K. Fukuda, Unfolding 3- dimensional convex polytopes: A package for Mathematica 1.2 or 2.0, Mathematica Notebook, University of Tokyo, 1993.
23. C. Schevon and J. O'Rourke, A conjecture on random unfoldings, Technical report JHU-87/20, Johns Hopkins University, Baltimore, MD, 1987.
24. M. Sharir and A. Schorr, On shortest paths in polyhedral spaces, SIAM J. Comput., 15:193-215, 1986.
25. G. C. Shephard, Convex polytopes with convex nets, Math. Proc. Camb. Phil. Soc., 78:389-403, 1975.
26. I. Wegener, Branching programs and binary decision diagrams, Monographs on discrete mathematics and applications, 2000.