Meissner Tetrahedron
The Meissner Tetrahedron is a body of constant width.
That means, you can use it to roll a plane on it like on a ball, and the distance keeps the same.
From the look of the somewhat irregular shape you might think that would be a bumpy ride, but it ist not!
Here's a nice explanation on those bodies:
http://www.youtube.com/watch?v=cUCSSJwO3GU