A modern classic for your desk, in a smoothed variant!
The Barth Sextic is the most famous example of the sometimes so-called world record surfaces. W. Barth constructed it around 1995. Its most striking geometric feature is the high symmetry; in fact, it has the same symmetry planes as a regular icosahedron.
This Barth Sextic is the holder of the world-record for the number singularities (special points) on so-called sextic surfaces. For our object we thickened all 50 singularities (the thin points) of the model a little; an actual singularity would be an infinitely thin connection between two parts, but such a sculpture would fall apart.
If you want to go for the really singular surface then you will have to choose another production method, e.g. laser-in-glass. See MO-Labs.com
for models of this type.