Name
Abstract | ||
|---|---|---|
UNFOLDING A CONVEX POLYHEDRON INTO A SIMPLE PLANAR POLYGON IS A WELL-STUDIED PROB-LEM. IN THIS PAPER, WE STUDY THE LIMITS OF UNFOLDABILITY BY STUDYING NONCONVEX POLY-HEDRA WITH THE SAME COMBINATORIAL STRUCTURE AS CONVEX POLYHEDRA. IN PARTICULAR, WE GIVE TWO EXAMPLES OF POLYHEDRA, ONE WITH 24 CONVEX FACES AND ONE WITH 36 TRIANGULAR FACES, THAT CANNOT BE UNFOLDED BY CUTTING ALONG EDGES. WE FURTHER SHOW THAT SUCH A POLYHEDRON CAN INDEED BE UNFOLDED IF CUTS ARE ALLOWED TO CROSS FACES. FINALLY, WE PROVE THAT \OPEN" POLYHEDRA WITH TRIANGULAR FACES MAY NOT BE UNFOLDABLE NO MATTER HOW THEY ARE CUT. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1016/S0925-7721(02)00091-3 | Computational Geometry: Theory and Applications |
Keywords | DocType | Volume |
convex face,nonconvex polyhedron,simple planar polygon,ununfoldable polyhedron,convex polyhedron,combinatorial structure,discrete geometry,unfolding polyhedra,well-studied problem,triangular face,nets | Journal | 24 |
Issue | ISSN | Citations |
2 | Computational Geometry: Theory and Applications | 21 |
PageRank | References | Authors |
2.18 | 11 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marshall Bern | 1 | 1642 | 229.86 |
| Erik D. Demaine | 2 | 4624 | 388.59 |
| David Eppstein | 3 | 4897 | 533.94 |
| Eric Kuo | 4 | 67 | 8.76 |
| Andrea Mantler | 5 | 82 | 6.54 |
| Jack Snoeyink | 6 | 2842 | 231.68 |