Examples of Fold-and-Cut

The crease patterns below all have the property that, when folded up, a single complete straight cut simultaneously cuts all the bold lines and no more, producing the desired shape or shapes. For more information, refer to the fold-and-cut problem and its mathematics. These examples were designed using the straight-skeleton method by Erik Demaine and Martin Demaine.

MIT Logo


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Thanks to Nina Strohminger for finding a good folding of this model.

Swan


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Angelfish


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Butterfly


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Fancy Star


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Based on a design by magician Gerald Loe in his book “Paper Capers” (1955).

G4G5 (prepared for the 5th Gathering for Martin Gardner)


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Jackolantern (make out of orange paper!)


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Entire Tangram Set from a Square


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How To Print

How To Fold

To fold one of these examples, we recommend the following procedure:

  1. Print the crease pattern as large as possible, and possibly also photo-enlarge using a photocopier onto larger paper.
  2. If your example has a central line of symmetry, fold along that first.
  3. Precrease all the creases (dashed and dot-dashed lines) by pinching the paper and ensuring that you follow along the printed lines, naturally forming a mountain crease. (This may get your hands a little dirty with toner.)
  4. Reverse the valley (dashed) creases, so that all crease have their proper orientation.
  5. Now the hard part: collapse all the creases simultaneously. This can take some practice, especially on the harder examples, but with some effort you should be able to get it.
  6. Finally, cut along the bold line.

Last updated January 22, 2012 by Erik Demaine.