What properties must a smoothly spinning toy top have? It would seem that there is some open source software that would allow you to create objects of a certain volume, even with arbitrary shape (I'm thinking blender and some of it's addons.)
Now, I know that, to spin, a top has to be symmetrical.  However, does is have to be radially symmetric?  (Or how close does it have to be?)  
I think I saw a top that consisted of a long spindly basketball player being spun (but if you saw all the empty space it was radially symmetric at most angles.)
I'm not a math genius but I did just barely survive 10 credit hours of calculus based physics, so if you are willing to explain it a bit I'll knock myself out...
 A: The center of mass must be directly above the point of rotation on the table. Otherwise, the top will wobble. But wobble can be “stable” state as well (see “nutation”), if the point on the table is fixed (i.e. there is enough friction to prevent slipping). In theory, this means that many odd, non-symmetrical shapes could spin smoothly, but in practice it might be difficult to get a non-symmetrical shape going. Think about spinning a quarter on a table: you can get it going nicely, but it might take a few tries. 
A: To spin smoothly, the line connecting the center of mass with the point upon which the top will spin must coincide with a principal axis (any rigid body has 3 mutually perpendicular principal axes; when and only when it rotates around one of them, the angular velocity and angular momentum vectors are parallel).  Also, I think it has to be either the principle axis about which the body has the largest or smallest moment of inertia--it won't work if it's the one with the intermediate moment of inertia.
