Anyone ever hear of a geometrical object called "superegg"? It was
supposed to behave like a rolling ball (stable in any position), yet be
oblong like an egg.
I always wanted to try making one, but never found more info than the
second-hand story I heard.
Thinking out loud: perhaps this could be done with a hollow wooden shell
which contains a steel ball. If I assume that the outside surface is a
revolution of an ellipse, and assume a steel sphere is inside, then I can
write a piece of code which will piece-wise calculate a thickness profile
where the C.G. of the hollow shell always balances the C.G. of the
off-center steel ball, with the tangent point (where the shell rests on
the table) acting as the fulcrum. If the C.G. of the assembly never
changes height, the oblong device would be stable regardless of
orientation.