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Rules for folding polyminoes from one level to two levels
Elizabeth Wilcox, Julia Martin
Polyominoes have been the focus of many recreational and research investigations.  In this article, the authors investigate whether a paper cutout of a polyomino can be folded to produce a second polyomino in the same shape as the original, but now with two layers of paper.  For the folding, only «corner folds» and «half edge cuts» are allowed, unless the polyomino forms a closed loop, in which case one is allowed to completely cut two squares in the polyomino apart.  With this set of allowable moves, the authors present algorithms for folding different types of polyominoes and prove that certain polyominoes can successfully be folded to two layers.  The authors also establish that other polyominoes cannot be folded to two layers if only these moves are allowed.
folding polyominoes
Published: 2018/01/11
Author Details
Elizabeth Wilcox
Mathematics Department, Oswego State University of New York

Julia Martin
Mathematics Department, Oswego State University of New York

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