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Nets References

Nets: References


Agarwal, P. and B. Aronov, J. O'Rourke, C. Schevon, Star unfolding of a polytope with applications, SIAM J. Computing, 26 (1997) 1689-1713.

Aleksandrov, A. and V. Zalgaller, Intrinsic Geometry of Surfaces, American Mathematical Society, Providence, 1967.

Alexandrov, A., Konvexe Polyeder, Akademie-Verlag, Berlin, 1958.

Aronov, B. and J. O'Rourke, Nonoverlap of the star unfolding, Discrete Computational Geometry, 8 (1992) 219-250.

Biedl, T., and E. Demaine, M. Demaine, A. Lubiw, J. O'Rourke, M. Overmars, S. Robbins, and S. Whitesides, Unfolding some classes of orthogonal polyhedra, in Proc. 10th Canadian Conference on Computational Geometry, 1998, pp. 70-71.

Bern, M., and E. Demaine, D. Eppstein, E. Kuo, Ununfoldable polyhedra, in Proc. 11th Canadian Conference on Computational Geometry, 1999, pp. 13-16.

Bouzette, S., and F. Buekenhout, D. Edmond, and A. Gottcheiner: A theory of nets for polyhedra and polytopes related to incidence geometry, Designs, Codes and Cryptography, 10 (1997) 115-136.

Buekenhout, F. and M. Parker, The number of nets of the regular convex polyhedra in dimension, preprint, 1996.

Dürer, A., Unterweisung der Messung mit dem Zirkel und Richtscheit, 1525. English translation and commentary, W. Strauss, The Painter's Manual, Abaris, New York, 1977.

Field, J., The Invention of Infinity: Mathematics and Art in the Renaissance, Oxford U. Press, Oxford, 1997.

Grünbaum, B., Nets of polyhedra, Geombinatorics 1 (1991) No. 2, 5-10.

Grünbaum, B., Nets of polyhedra II, Geombinatorics 1 (1991) No., 3, 5-10.

Grünbaum, B., A starshaped polyhedron with no net, Geombinatorics 11 (2001) 43-48.

Lubiw, A. and J. O'Rourke, When can a polygon fold to a polytope? Technical Report 48, Department of Computer Science, Smith College, June, 1996.

Namiki, M. and K. Fukuda, Unfolding 3-dimensional convex polytopes: A package for Mathematica, Mathematica Notebook, University of Tokyo, 1993.

O'Rourke, J., Folding and unfolding in computational geometry, in Proc. Japan Conference on Discrete and Computational Geometry, 1998, Volume 1763, Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, 2000, p. 258-266.

Reggini, H., Regular polyhedra: random generation, Hamiltonian paths and single chain nets. Monografias de la Academia Nacional de Ciencias
Exactas, Fiscas y Naturales; No. 6. Buenos Aires, 1991.

Schevon, C., Algorithms for Geodesics on Polytopes, PhD Thesis, Johns Hopkins University, Baltimore, 1989.

Schevon, C. and J. O'Rourke, A conjecture on random unfoldings, Technical Report JHU-87/20, John Hopkins University, Baltimore, 1987.

Schlickenrieder, W., Nets of Polyhedra, Thesis, Technische Universität Berlin, 1997.

Shephard, G., Convex polytopes with convex nets, Math. Proc. Camb. Phil. Soc. 78 (1975) 389-403.

Tarasov, A., Polyhedra with no natural unfolding, Russian Mathematical Surveys 54 (1999) 656-657.

An expository article about unfolding polyhedra that I wrote in English appears in French:

Le géomètre et la paire de ciseaux, La Recherche, October, 2001, Number 346, p. 62-63.

A web link to an English translation of the article above.

Some web resources about unfoldings.

This link provides some diagrams and results related to unfoldings and conjectures about unfolding.

A link where Schlickenrieder's thesis on unfoldings can be downloaded. (Links on the upper right of the page go to the thesis.)

This page of Jeff Erickson has interesting background about unfolding problems.

This page of Joseph O'Rourke has a variety of items related to unfolding issues, including papers that can be downloaded.