Common unfoldings of polyominoes and polycubes
Name
Demaine-Common unfoldings.pdf
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2.69 MB
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Author(s)
Aloupis, Greg
Bose, Prosenjit
Collette, Sebastien
Demaine, Erik D.
Demaine, Martin L.
Douieb, Karim
Dujmovic, Vida
Iacono, John
Langerman, Stefan
Morin, Pat
Date Issued
November 2011
Journal
Computational Geometry, Graphs and Applications
Publisher
Springer Berlin / Heidelberg
Citation
Aloupis, Greg et al. “Common Unfoldings of Polyominoes and Polycubes.” Computational Geometry, Graphs and Applications. Ed. Jin Akiyama et al. LNCS Vol. 7033. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. 44–54.
Version
Author's final manuscript
Abstract
This paper studies common unfoldings of various classes of polycubes, as well as a new type of unfolding of polyominoes. Previously, Knuth and Miller found a common unfolding of all tree-like tetracubes. By contrast, we show here that all 23 tree-like pentacubes have no such common unfolding, although 22 of them have a common unfolding. On the positive side, we show that there is an unfolding common to all “non-spiraling” k-ominoes, a result that extends to planar non-spiraling k-cubes.
Description
Computational Geometry, Graphs and Applications 9th International Conference, CGGA 2010, Dalian, China, November 3-6, 2010, Revised Selected Papers
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/978-3-642-24983-9_5
