Math Monday: Folding Challenge – Can you do It?

by Glen Whitney



How would you like to make something like this?

boypapermodel_tiny

That’s a paper model of a polyhedral version of the “Boy’s surface” — the key half-way point in a singularity-free eversion of a sphere. (Eversion simply means “turning inside out,” like you would a sock or a t-shirt. Of course, a sphere has to intersect itself to be turned inside out in three dimensions.) And it was created by Konrad Polthier, who wrote an article about it an lots of other folding things. Here are a couple of examples:

venusunfold0001_smlcatenoidunfold0000_tiny

Your challenge, should you choose to accept it, is to use the information in the article to construct an actual physical model of one of the more interesting shapes or surfaces featured there, and send a photo to mondays@momath.org — if enough photos come that way, there will be a follow-up posting with some of the best. Good luck! (Some of those models are remarkably intricate — take a look and see.)

This article first appeared on Make: Online, November 25, 2013.

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