By George Hart for the Museum of Mathematics


You may know how to make a ship in a bottle, but how would you make this octahedron in a balloon? The twelve edges of the octahedron are made of strips of blue balloon rubber, glued to the inside of the clear balloon at the six vertices. Think of how you might make this before reading my solution below.

octahedron in balloon Math Monday: An Octahedron in a Balloon

I did it by first making a spherical octahedron on the outside of the balloon. It is glued with rubber cement at the six cardinal points: top, bottom, left, right, front, back.

img 1467 Math Monday: An Octahedron in a Balloon

Then I untied the slip knot to let the air out of the balloon, carefully turned it inside out, and reinflated it.

img 1468 Math Monday: An Octahedron in a Balloon

If you master this technique, the next step is to try to make a nice cube. And be sure to send me a photo if you can make the compound of five tetrahedra in five different colors.

See all of George Hart’s Math Monday columns

Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.

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