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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Common Unfoldings of Polyominoes and Polycubes
verfasst von : Greg Aloupis, Prosenjit K. Bose, Sébastien Collette, Erik D. Demaine, Martin L. Demaine, Karim Douïeb, Vida Dujmović, John Iacono, Stefan Langerman, Pat Morin
Erschienen in: Computational Geometry, Graphs and Applications
Verlag: Springer Berlin Heidelberg
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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.