Here is a curious thing for a weekend project. It is called a rattleback. If you try and spin it, it will wobble and rattle until it changes direction and spins the other way. It will spin fine one way but not the other. (Another one of my student demonstrations.) It is a forgiving double sided carve since the sides do not need to line up exactly. If you have a nice small piece of exotic wood (denser is better), this is the perfect use for it. There are two versions, one nice and smooth and the other a "voodoo" version. (The pictures are of a smooth one made of rose wood and lacquered.) They are very easy to finish and make great little gifts.
This is my own mathematical surface that I created in a math program called Maple. Imported using the STL importer.
http://youtu.be/OHCc22r329Q