Unistable Polyhedron

by jbrownkramer, published

Unistable Polyhedron by jbrownkramer May 18, 2013
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1002Views 366Downloads Found in Math


When printed at a uniform density (i.e. filled in, not hollow), this polyhedron has the property that it is only stable on one face. That is, it will always topple over an land on one side.

I have not had an opportunity to print them out, so I don't know if they work in practice. My understanding is that they are fairly sensitive to inaccuracies. I have provided a version of the polyhedron that is split in two, in the hope that it will print more accurately and can be glued together.

The existence of these polyhedra was first proven by Conway and Guy.

This particular one was taken from the mathematica notebook found at the article by Pegg, Ed Jr. and Weisstein, Eric W. "Unistable Polyhedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/UnistablePolyhedron.html

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