I tried the Icosahedron that Five posted. It's so much tougher to build than it looks. I changed a few thing to make it more stable and not require the full sphere for support. Using 2 2x2 dishes per node, the pin joints almost click into place.
The 4x4 dishes also needed to be 1 more plate above the the 2x2 dish (in the original that Five posted) so that they don't interfere with each other. The way I did it doesn't need an extra plate.