Common unfoldings of polyominoes and polycubes
Author(s)Aloupis, Greg; Bose, Prosenjit; Collette, Sebastien; Demaine, Erik D.; Demaine, Martin L.; Douieb, Karim; Dujmovic, Vida; Iacono, John; Langerman, Stefan; Morin, Pat; ... Show more Show less
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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.
Computational Geometry, Graphs and Applications 9th International Conference, CGGA 2010, Dalian, China, November 3-6, 2010, Revised Selected Papers
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Computational Geometry, Graphs and Applications
Springer Berlin / Heidelberg
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.
Author's final manuscript