Folding Polyominoes with Holes into a Cube

10/22/2019

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When can a polyomino piece of paper be folded into a unit cube? Prior work studied tree-like polyominoes, but polyominoes with holes remain an intriguing open problem. We present sufficient conditions for a polyomino with one or several holes to fold into a cube, and conditions under which cube folding is impossible. In particular, we show that all but five special simple holes guarantee foldability.

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Folding Polyominoes with Holes into a Cube

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Folding Polyominoes with Holes into a Cube

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