<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

Rules for folding polyminoes from one level to two levels

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Rules for folding polyminoes from one level to two levels"}

Polyominoes have been the focus of many recreational and research investigations. In this article, the authors investigate whether a paper cutout of a...

Rules for folding polyminoes from one level to two levels

Published Online: Jan 11, 2018

Page range: 47 - 58

DOI: https://doi.org/10.1515/rmm-2017-0020

Keywords
Folding polyominoes

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Rules for folding polyminoes from one level to two levels

Published Online: Jan 11, 2018

Page range: 47 - 58

DOI: https://doi.org/10.1515/rmm-2017-0020

KeywordsFolding polyominoes

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Folding polyominoes