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To: Sun Tzu who wrote (1)	6/27/2025 7:28:43 AM
From: Sun Tzu	of 3

There's a neat video of the constructed tetrahedra at the link. "The great mathematician John Conway was interested not only in how tetrahedra can be arranged or rearranged, but also in how they balance. In 1966, he and the mathematician Richard Guy asked whether it was possible to construct a tetrahedron made of a uniform material — with its weight evenly distributed — that can only sit on one of its faces. If you were to place such a “monostable” shape on any of its other faces, it would always flip to its stable side. A few years later, the duo answered their own question, showing that this uniform monostable tetrahedron wasn’t possible. But what if you were allowed to distribute its weight unevenly? At first, it might seem obvious that this should work. “After all, this is how roly-poly toys work: Just put a heavy weight in the bottom,” said Dávid Papp(opens a new tab) of North Carolina State University. But “this only works with shapes that are smooth or round or both.” When it comes to polyhedra, with their sharp edges and flat faces, it’s not clear how to design something that will always flip to the same side." quantamagazine.org.

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