Clebsch's Diagonal Cubic Surface is probably THE most famous mathematical model. Since its first construction in 1872 by hand in plaster, it made its way to numerous collections of mathematical models.
In contrast to the historical objects, our modern version only consists of a thin surface and not a hole body of plaster; which is much closer to the abstract mathematical object and which makes it much easier to see important geometrical properties of the object, such as its "holes" and "tunnels".