I nearly voted for two, but decided that, as solids, the icosahedron definitely just edges it. If you get to compare the unfolded versions too then the dodecahedron is pretty damned good though.

PS, I like the spinning effect on your apps, with the different speeds depending on how hard you tugged them!

Thank you! It wasn't a new idea of mine – the MathWorld ones do the same, though the response isn't as smooth and they stop moving as soon as the mouse pointer goes outside their containing box – but I was pleased with how it came out when I tried it.

Yes I like the net of the dodecahedron :)