Enumerating foldings and unfoldings between polygons and polytopes

Graphs and Combinatorics

Volumn 18, Issue 1, 2002, Pages 93-104

  Demaine, Erik D ^a   Demaine, Martin L ^a   Lubiw, Anna ^b   O'Rourke, Joseph ^c  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

^c SMITH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036972784     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003730200005     Document Type: Article

References (10)

1. Agarwal, P.K., Aronov, B., O'Rourke, J., Schevon, C.A.: Star unfolding of a polytope with applications. SIAM J. Comput., 26, 1689-1713 (1997)
2. Aleksandrov, A.D.: Konvexe Polyeder. Berlin, Germany: Akademie-Verlag 1958
3. Aronov, B., O'Rourke, J.: Nonoverlap of the star unfolding. Discrete Comput. Geom., 8, 219-250 (1992)
4. Biedl, T., Demaine, E.D., Demaine, M.L., Lubiw, A., O'Rourke, J., Overmars, M., Robbins, S., Whitesides S.: Unfolding some classes of orthogonal polyhedra. In: Proc. 10th Canad. Conf. Comput. Geom., pp. 70-71, 1998
5. Bern, M., Demaine, E.D., Eppstein, D., Kuo, E., Mantler, A., Snoeyink, J.: Ununfoldable polyhedra with convex faces. Comput. Geom. Theory Appl., to appear (2001) (Full version: ArXive cs.CG/9908003)
6. Demaine, E.D., Demaine, M.L., Lubiw, A., O'Rourke, J.: Examples, counterexamples, and enumeration results for foldings and unfoldings between polygons and polytopes. Technical Report 069, Smith College, Northampton, MA 2000 (ArXive cs.CG/ 0007019)
7. Hirata, K.: Personal communication, 26 June 2000. Dept. Math., Ehime University, Japan 2000 (http://weyl.ed.ehime-u.ac.jp/cgi-bin/WebObjects/Polytope2)
8. Lubiw, A., O'Rourke, J.: When can a polygon fold to a polytope? Technical Report 048, Dept. Comput. Sci., Smith College 1996. Presented at AMS Conf., 1996
9. O'Rourke, J.: Folding and unfolding in computational geometry. In: Proc. Japan Conf. Discrete Comput. Geom. '98, volume 1763 of Lecture Notes Comput. Sci., pp. 258-266, Springer-Verlag 2000
10. Shephard, G.C.: Convex polytopes with convex nets. Math. Proc. Camb. Phil. Soc., 78, 389-403 (1975)