One-Zipper Unfoldings of 3D Shapes

Craft & Design Science
One-Zipper Unfoldings of 3D Shapes

Just discovered this fascinating little geometrical recreation at the 2011 Bridges Math Art Conference galleries. The idea is simple, and the field still fairly unexplored, from what I can tell. What interesting 3D shapes can be made by zipping up the edges of a planar shape using a single zipper?

A bit of Googling brought me to the homepage of Macarthur fellow Erik D. Demaine, whose work in origami and other geometrical fields we have featured here many times before. You can click on his name at the bottom of this post to see our aggregated past coverage of Erik’s work.

Erik’s page has lots of videos showing the unfolding and folding processes, and reveals a useful trick for researchers: To find out if a shape has a zipper unfolding, just make a 3D paper model and then cut along the edges with a knife—if you can completely flatten the shape with one continuous, non-backtracking cut, the path represents a zipper unfolding of that shape.

Besides making interesting intellectual problems, zipper unfoldings have many cool potential crafty applications as purses, bags, pillows, etc. With sufficiently rigid or reinforced fabric and the right shape, one might even make a zip-up chair, stool, table, or other furniture this way.

2 thoughts on “One-Zipper Unfoldings of 3D Shapes

  1. Al Roderick says:

    Hmm. Now, a practical application might be an icosahedral bag for a round object, like a sports ball or piece of fruit, that can fold up into a little triangle when it isn’t in use. If there was a reliable way to make a zipper watertight I might go for a collapsible spherical waterskin. Maybe a plastic liner with a neck that can simply roll up, and the polyhedron is made of an insulating and structural material like neoprene?

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I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I am a long-time contributor to MAKE magazine and My work has also appeared in ReadyMade, c't – Magazin für Computertechnik, and The Wall Street Journal.

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