#MathArtChallenge 100: Balloon Polyhedra

In the first, allow me to thank each and every one of you who has participated in the #MathArtChallenge in the last few months. This is my “last” post. Meaning, I don’t promise to make more Math Art Challenges, but there’s always the chance that something will come up…

All of the #MathArtChallenge-s will continue to be up on this blog, and I really hope that you’ll make use of them in your classes or in your fun time or however brings you joy.

The Challenge: Today, you get Balloon Polyhedra. There’s actually several papers written about this, so go check them out.

Materials needed: Twisting balloons, pump, patience
Math concepts you could explore with this challenge: angles, arithmetics, counting, geometry, graph theory, polygons, polyhedra, symmetry, vertices/intersections

I intended to make all the Platonic solids and all the Archimedean solids, but frankly, after what I did do today, my hands are sore from tying and the balloons didn’t fit in my house any more.

I also intended to take some videos of these, but there are few unbreakable rules in the universe and one of them is: when the neighbor kid sees your balloons, you have to give them to her. (She wore them all in outfits and was just gleeful. It was pretty great to see.)

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

1.) Make sense of problems and persevere in solving them. How many balloons are needed for each structure? How will you connect them such that you don’t have the balloons double-backing on themselves?

6.) Attend to precision. In creating the models, you’ll have to pay close attention to how each balloon is segmented and which segments connect in which ways to other balloons.

7.) Look for and make use of structure. These often require some serious planning, but their creation leans on your understanding of and the understanding you build of the structure of the edges and vertices of the various solids.