  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.
