Can three screw-shaped pieces plus another with tri-lateral symmetry be assembled into an octahedron? It doesn't seem likely, yet the assembly even interlocks solidly. The assembled puzzle makes a nice top which spins smoothly without falling apart. Made from 13mm hollow spheres.
This puzzle is ideal for 3D printing. It would be very difficult to make it out of wood due to the complex 3D shape of the pieces and the slight flexibility needed. Wood pieces tend to break.
This was my exchange puzzle at the 30th International Puzzle Party in July, 2010.