I was recently reminded of the gömböc (pronounced: ‘goemboets’). It is a three dimensional shape that, when placed on a flat surface always comes to rest in the same position no matter how you place it. More technically it is (the first known) homogenous object with one stable and one unstable equilibrium point. That’s pretty cool.
There are plenty of pictures, videos and discussions found by searching on Gömböc.