Gömböc

A gömböc is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. The presence of only one stable and unstable equilibrium point in a gömböc means that it returns to one equilibrium position (the stable equilibrium point) no matter how it is pushed or turned around. The shape of the gömböc is actually mimicked in certain shelled animals, such as turtles, which when placed upside down can turn back (right themselves) immediately after. This is very important for their survival.

Here is an interesting video showing the development of the gömböc. It turns out to be a very difficult task, mathematically speaking.

https://www.youtube.com/watch?v=XOwez5hPuiA