Common unfoldings of polyominoes and polycubes

Authors:
Greg Aloupis;Prosenjit K. Bose;Sébastien Collette;Erik D. Demaine;Martin L. Demaine;Karim Douïeb;Vida Dujmović;John Iacono;Stefan Langerman;Pat Morin
Affiliations:
Academia Sinica, Taiwan;Carleton University, Canada;Université Libre de Bruxelles, Belgium;Massachusetts Institute of Technology;Massachusetts Institute of Technology;Carleton University, Canada;Carleton University, Canada;Polytechnic Institute of New York University;Université Libre de Bruxelles, Belgium;Carleton University, Canada
Venue:
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Year:
2010

Citing 3
Cited 0

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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.