Re: [math-fun] Polyhedral center-of-gravity problem

Which brings up the old problem: Does there exist a polyhedron with no stable face on a tabletop? (I.e., for which the center-of-gravity's projection to the plane of any face lies outside that face.) The standard argument for why no such polyhedron exists is that it would keep rolling forever, so be a perpetual motion machine. Some time ago there was no known proof purely by geometry. Does anyone know if that's still the case? --Dan On 2012-09-20, at 9:32 PM, Brent wrote:

And whether the projection of the CG onto the plane of the face falls within the face. :-)