Math Monday: Tensegrity Balls

Craft & Design
Math Monday: Tensegrity Balls

By George Hart for the Museum of Mathematics


Here is a bouncy structure made of dowels and rubber bands in which no sticks directly touch each other. The compression members are not connected, yet the entire structure supports compression, which is an unusual property often called “tensegrity.” In this example, the thirty sticks follow the edges of a dodecahedron, so there are twelve five-fold spirals.

Symmetric models of this sort are easy to make from dowels and rubber bands. Here, I cut small slits at each end of 3/16 dowels to hold standard office rubber bands.

The basic unit is one dowel holding a rubber band stretched between its two slots, as seen at the lower left below. Start by making the cycle of five units shown. Join units by connecting a slot to the rubber band of another dowel, roughly at the one-third point. Then add more units to make large triangles using the two-thirds left over from each rubber band. The unconnected unit below is positioned to be connected in two places to make such a triangle. Follow this pattern everywhere and the ball builds itself. The twelve pentagons will all spiral with the same handedness, each one third of a stick in length.

See all of George Hart’s Math Monday columns

6 thoughts on “Math Monday: Tensegrity Balls

  1. First L says:

    So what happens if you cut one of the rubber bands?

    1. Anonymous says:

      This YouTube Video shows what happens to a spherical tensegrity after several tendons are cut (one by one). Thanks to the YouTube user “bkesty” for sacrificing his model in this wonderful demonstration.

      Marcelo Pars just updated his tensegrity model website with some beautiful helical and butterfly-like tensegrity artwork.

      I am fond of models created at higher tension: they are capable of carrying much larger loads than rubber-band models. I have published a proposal for DIYers to create a “factory” capable of making high-tension six-strut tensegrity models at the website .

  2. francescodifusco says:

    Reblogged this on FRANCESCO DI FUSCO.

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Gareth Branwyn is a freelance writer and the former Editorial Director of Maker Media. He is the author or editor of over a dozen books on technology, DIY, and geek culture. He is currently a contributor to Boing Boing, Wink Books, and Wink Fun. And he has a new best-of writing collection and “lazy man’s memoir,” called Borg Like Me.

View more articles by Gareth Branwyn
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