Unistable polyhedra

Monday 29 August 2005This is almost 18 years old. Be careful.

These days, Kellogg’s cereals have Disney wobblers in them. Because of their round bottoms and a very low center of gravity, they wobble but end up standing upright. I was discussing this with Max, who had lots of questions about center of gravity. Could you make an object with a center of gravity on the ground? No, because some of the mass has to be on the other side of any line drawn through the center of gravity.

Then I remembered something I’d read about a long time ago. A few searches, and I found it: a unistable polyhedron is one which will only rest on one of its faces. Robert Dawson calls them by a different name, but has some nice pictures: monostatic polytopes.

In the real world, there’s a very pragmatic reason to be concerned about polyhedral stability: it is at the heart of the issue of Fair Dice.


Regarding the center of gravity on the ground, boats are a fairly analogous situation and perhaps a good place to take the conversation; they take on ballast to lower their center of gravity which in turn increases their stability and so on...

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