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Joseph O\'Rourke also wrote an article describing these results, ``Computational Geometry Column 39,\'\' International Journal of Computational Geometry and Applications, 10(4):441-444, 2000.",
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Helen Pearson also wrote an article describing these results, ``Origami solves road map riddle,\'\' Nature Science Update, February 18, 2002.",
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This version is updated from the original conference version in order to fix an error discovered by and solved together with Thomas Shermer.",
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John Conway\'s Holyhedron Problem has been solved by Jade Vinson in “On Holyhedra” (with an introduction by John Conway), Discrete and Computational Geometry, volume 24, number 1, pages 85-104, 2000. There is still work to be done in order to win the $10,000 / (number of faces) reward, because Vinson\'s polyhedron has 78,585,627 faces and genus 60,380,421! Don Hatch reports some further progress: a 492-face holyhedron.
John Conway\'s Angel and Devil Problem has been solved, even for power-2 angel, by András Máthé and Oddvar Kloster. See this blog post. There are other solutions, for higher-power angels, by Brian Bowditch and Peter Gács.",
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"comments" : "This paper is also available as arXiv:cs.CG/9910009 of the Computing Research Repository (CoRR).",
"month" : "October",
"type" : "Publication",
"year" : "1999",
"label" : "Locked and Unlocked Polygonal Chains in 3D",
"key" : "3DChainsTR",
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},
{
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"Demaine, Erik D.",
"O\'Rourke, Joseph"
],
"comments" : "This paper is also available from the electronic proceedings as http://www.cs.ubc.ca/conferences/CCCG/elec_proc/open.ps.gz.",
"month" : "August 15--18",
"type" : "Publication",
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"address" : "Vancouver, British Columbia, Canada",
"key" : "CCCG99Open",
"bookurl" : "http://www.cs.ubc.ca/conferences/CCCG/",
"papers" : "CCCCG2006Open; CCG2005Open; CCCG2004Open; CCCG2003Open; CCCG2002Open; CCCG2001Open; CCCG2000Open; CCCG99OpenTR"
},
{
"type" : "Publication",
"author" : [
"Demaine, Erik D.",
"Demaine, Martin L.",
"Eppstein, David",
"Friedman, Erich"
],
"length" : "15 pages",
"address" : "Vancouver, British Columbia, Canada",
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"comments" : "This paper is also available from the electronic proceedings as http://www.cs.ubc.ca/conferences/CCCG/elec_proc/fp37.ps.gz. It is also available as arXiv:cs.CG/9970183v1 of the Computing Research Repository (CoRR).",
"label" : "Hinged Dissection of Polyominoes and Polyiamonds",
"bookurl" : "http://www.cs.ubc.ca/conferences/CCCG/",
"updates" : "There is a revised paper with new results and a new coauthor (Greg Frederickson).",
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{
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"date" : "1999-08",
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"author" : [
"Bern, Marshall",
"Demaine, Erik D.",
"Eppstein, David",
"Kuo, Eric"
],
"comments" : "This paper is published in CCCG\'99.
It is also available as arXiv:cs.CG/9908003v1 of the Computing Research Repository (CoRR).",
"month" : "August",
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},
{
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"Bern, Marshall",
"Demaine, Erik D.",
"Eppstein, David",
"Kuo, Eric"
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"comments" : "This paper is also available from the electronic proceedings as http://www.cs.ubc.ca/conferences/CCCG/elec_proc/fp38.ps.gz.
It is also available as version 1 of arXiv:cs.CG/9908003 of the Computing Research Repository (CoRR).",
"label" : "Ununfoldable Polyhedra",
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"updates" : "We have solved some of the open problems mentioned in this paper; see the CGTA paper.",
"pages" : "13--16",
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{
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"author" : [
"Brodnik, Andrej",
"Carlsson, Svante",
"Demaine, Erik D.",
"Munro, J. Ian",
"Sedgewick, Robert"
],
"type" : "Publication",
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"label" : "Resizable Arrays in Optimal Time and Space",
"key" : "ResizableArraysTR",
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},
{
"copyright" : "The paper is \\copyright Springer-Verlag.",
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"Brodnik, Andrej",
"Carlsson, Svante",
"Demaine, Erik D.",
"Munro, J. Ian",
"Sedgewick, Robert"
],
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"label" : "Resizable Arrays in Optimal Time and Space",
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},
{
"copyright" : "The paper is \\copyright Springer-Verlag.",
"type" : "Publication",
"author" : [
"Benoit, David",
"Demaine, Erik D.",
"Munro, J. Ian",
"Raman, Venkatesh"
],
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"comments" : "This paper is also available from the electronic LNCS volume as http://link.springer.de/link/service/series/0558/papers/1663/16630169.pdf.",
"label" : "Representing Trees of Higher Degree",
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},
{
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"pages" : "91--100",
"date" : "1999-07",
"author" : [
"Demaine, Erik D.",
"Demaine, Martin L.",
"Lubiw, Anna"
],
"comments" : "To keep the file smaller, the paper does not include the photographs in Figures 5, 6, and 7. Please refer to my hypar webpage to see these photographs.
Here are some photographs from during and after my talk, taken by Carlo Séquin.
![](\"hypartalk1s.jpg\")
![](\"hypartalk2s.jpg\")
",
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"type" : "Publication",
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"label" : "Polyhedral Sculptures with Hyperbolic Paraboloids",
"updates" : "Ivars Peterson describes these results in his book, Fragments of Infinity: A Kaleidoscope of Math and Art, John Wiley & Sons, Inc., 2001, pages 79-80.",
"address" : "Winfield, Kansas",
"key" : "BRIDGES99",
"bookurl" : "http://www.sckans.edu/ bridges/"
},
{
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"Erickson, Jeff"
],
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"label" : "Open Problems on Polytope Reconstruction",
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},
{
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"pages" : "409--410",
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"author" : [
"Demaine, Erik",
"Demaine, Martin",
"Lubiw, Anna",
"O\'Rourke, Joseph",
"Pashchenko, Irena"
],
"month" : "June 13--16",
"webpages" : "metamorphosis",
"type" : "Publication",
"year" : "1999",
"label" : "Metamorphosis of the Cube",
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},
{
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"Demaine, Erik D.",
"Demaine, Martin L.",
"Mitchell, Joseph S. B."
],
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"Biedl, Therese C.",
"Demaine, Erik D.",
"Lazard, Sylvain",
"Robbins, Steven M.",
"Soss, Michael A."
],
"month" : "March",
"webpages" : "linkage",
"type" : "Publication",
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"label" : "Convexifying Monotone Polygons",
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},
{
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"Demaine, Martin L.",
"Lubiw, Anna"
],
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"webpages" : "foldcut",
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"label" : "Folding and One Straight Cut Suffice",
"updates" : "Ivars Peterson wrote an article describing these results, ``Fold-and-Cut Magic,\'\' Science News 162(22), November 30, 2002.
Joseph O\'Rourke also wrote an article describing these results, ``Computational Geometry Column 36,\'\' International Journal of Computational Geometry and Applications, 9(6):615-618, 1999.",
"address" : "Baltimore, Maryland",
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},
{
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"pages" : "130--139",
"date" : "1999-01",
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"Biedl, Therese C.",
"Bose, Prosenjit",
"Demaine, Erik D.",
"Lubiw, Anna"
],
"month" : "January 17--19",
"award" : "Invited to special issue of \\emph{Journal of Algorithms}.",
"type" : "Publication",
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"label" : "Efficient Algorithms for Petersen\'s Matching Theorem",
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"papers" : "MatchingJAlgorithms"
},
{
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"length" : "2 pages; 20 minutes",
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"pages" : "866--867",
"date" : "1999-01",
"author" : [
"Biedl, T.",
"Demaine, E.",
"Demaine, M.",
"Lazard, S.",
"Lubiw, A.",
"O\'Rourke, J.",
"Overmars, M.",
"Robbins, S.",
"Streinu, I.",
"Toussaint, G.",
"Whitesides, S."
],
"comments" : "This paper is also available as arXiv:cs.CG/9811019 of the Computing Research Repository (CoRR).",
"month" : "January 17--19",
"type" : "Publication",
"year" : "1999",
"label" : "Locked and Unlocked Polygonal Chains in {3D}",
"address" : "Baltimore, Maryland",
"updates" : "The pocket-flipping algorithm described in this paper has been implemented by Jean-Philippe Cote and Marc-Andre Sauve as a course project for Godfried Toussaint. Their project web page includes the detailed history of the problem, and an applet to demonstrate the motion.",
"key" : "SODA99c",
"bookurl" : "http://www.siam.org/meetings/da99/",
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},
{
"copyright" : "The paper is \\copyright Springer-Verlag.",
"type" : "Publication",
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"Demaine, Erik D.",
"Demaine, Martin L.",
"Lubiw, Anna"
],
"length" : "15 pages",
"address" : "Tokyo, Japan",
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"comments" : "Shorter version in \\emph{Abstracts from the Japan Conference on Computational Geometry}, pages 5--9.",
"label" : "Folding and Cutting Paper",
"series" : "Lecture Notes in Computer Science",
"updates" : "Ivars Peterson wrote an article describing these results, ``Fold-and-Cut Magic,\'\' Science News 162(22), November 30, 2002.
Joseph O\'Rourke also wrote an article describing these results, ``Computational Geometry Column 36,\'\' International Journal of Computational Geometry and Applications, 9(6):615-618, 1999.",
"pages" : "104--117",
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"webpages" : "foldcut",
"bookurldead" : "http://ranran.cis.ibaraki.ac.jp/jcdcg98/jcdcg98.html",
"date" : "1998-12",
"month" : "December 9--12",
"seriesurl" : "http://www.springer.de/comp/lncs/",
"xeditor" : "Jin Akiyama and Mikio Kano and Masatsugu Urabe",
"key" : "JCDCG98"
},
{
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"Demaine, Martin L.",
"Mitchell, Joseph S. B."
],
"length" : "2 pages; 20 minutes",
"address" : "Providence, Rhode Island",
"uri" : "urn:d95bc3195c853a32adcaf6d75e7537c6",
"comments" : "Here is a bicolor flat origami I made for the talk.
(Photograph by Roberto Tamassia)
![](\"cgc98s.jpg\")
",
"label" : "Folding Any Silhouette from a Strip",
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"booktitle" : "Abstracts from the 3rd CGC Workshop on Computational Geometry (CGC\'98)",
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"date" : "1998-10",
"month" : "October 11--12",
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{
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"institution" : "Faculty of Computer Science, University of New Brunswick",
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"number" : "TR98-120",
"author" : [
"Demaine, Erik D.",
"L\\\'opez-Ortiz, Alejandro",
"Munro, J. Ian"
],
"year" : "1998",
"type" : "Publication",
"label" : "Adaptive Set Intersections",
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"talks" : "CodesTrees98",
"papers" : "SODA2000"
},
{
"copyright" : "The paper is \\copyright Springer-Verlag.",
"type" : "Publication",
"author" : [
"Demaine, Erik D.",
"Demaine, Martin L."
],
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"address" : "Montr\\\'eal, Qu\\\'ebec, Canada",
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"label" : "Planar Drawings of Origami Polyhedra",
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"series" : "Lecture Notes in Computer Science",
"pages" : "438--440",
"poster" : "1",
"year" : "1998",
"papers" : "DrawingExtremeTR",
"booktitle" : "Proceedings of the 6th Symposium on Graph Drawing (GD\'98)",
"volume" : "1547",
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"date" : "1998-08",
"month" : "August 13--15",
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"institution" : "Department of Computer Science, University of Waterloo",
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"author" : [
"Demaine, Erik D.",
"Demaine, Martin L."
],
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},
{
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"length" : "11 pages; 20 minutes",
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"uri" : "urn:869fade58f6d6b1d0044cc8a00c6eda0",
"date" : "1998-08",
"unrefereed" : "1",
"author" : [
"Biedl, Therese C.",
"Demaine, Erik D.",
"Demaine, Martin L.",
"Lubiw, Anna",
"Toussaint, Godfried T."
],
"comments" : "This paper is also available from the electronic proceedings as http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-hiding.ps.gz.",
"month" : "August 10--12",
"webpages" : "wrapping",
"type" : "Publication",
"year" : "1998",
"label" : "Hiding Disks in Folded Polygons",
"updates" : "One problem explored in this paper, packing the largest pair of equal-radius disks in a given polygon, have been further developed in several followup papers. See my webpage on wrapping for a summary and references.
Erin McLeish prepared an excellent webpage describing these and related results and algorithms, including a Java applet.",
"address" : "Montr\\\'eal, Qu\\\'ebec, Canada",
"key" : "CCCG98a",
"bookurl" : "http://cgm.cs.mcgill.ca/cccg98/"
},
{
"booktitle" : "Proceedings of the 10th Canadian Conference on Computational Geometry (CCCG\'98)",
"length" : "10 pages; 20 minutes",
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"date" : "1998-08",
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"Demaine, Erik",
"Demaine, Martin",
"Lubiw, Anna",
"Overmars, Mark",
"O\'Rourke, Joseph",
"Robbins, Steve",
"Whitesides, Sue"
],
"comments" : "This paper is also available from the electronic proceedings as http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-unfolding.ps.gz.",
"month" : "August 10--12",
"type" : "Publication",
"year" : "1998",
"label" : "Unfolding Some Classes of Orthogonal Polyhedra",
"address" : "Montr\\\'eal, Qu\\\'ebec, Canada",
"key" : "CCCG98b",
"bookurl" : "http://cgm.cs.mcgill.ca/cccg98/"
},
{
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"Biedl, Therese",
"Demaine, Erik",
"Demaine, Martin",
"Lazard, Sylvain",
"Lubiw, Anna",
"O\'Rourke, Joseph",
"Robbins, Steve",
"Streinu, Ileana",
"Toussaint, Godfried",
"Whitesides, Sue"
],
"length" : "11 pages; 20 minutes",
"address" : "Montr\\\'eal, Qu\\\'ebec, Canada",
"uri" : "urn:dba00787f3bf0bb239d164c6dc9db699",
"comments" : "This paper is also available from the electronic proceedings as http://cgm.cs.mcgill.ca/cccg98/proceedings/cccg98-biedl-reconfiguring.ps.gz.",
"label" : "On Reconfiguring Tree Linkages: Trees can Lock",
"bookurl" : "http://cgm.cs.mcgill.ca/cccg98/",
"year" : "1998",
"papers" : "LockedTreeDAM; LockedTreeTR",
"booktitle" : "Proceedings of the 10th Canadian Conference on Computational Geometry (CCCG\'98)",
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Further updates concerning this technical report:
- In joint work with Therese Biedl, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O\'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, and Sue Whitesides, it has been shown that general trees linkages cannot always be straightened (disallowing extra folds); see the CCCG\'98 paper. This solves the open problem mentioned in Section 5.3, but does not disprove the closed-chain conjecture as claimed in this technical report. In fact, the closed-chain conjecture is true; see my linkage webpage.
- In joint work with Marshall Bern, David Eppstein, and Barry Hayes, the first part of Conjecture 1 has been disproved: it is possible to combine several \"local\" bisector graphs (instead of using one \"global\" one) to solve the folding-and-cutting problem. See the FUN\'98 paper.
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