The rise of personal rapid prototyping machines, such as the Makerbot, RepRap, or Fab@Home, allows one to make a variety of geometric models. Polyhedral models, such as this 5 cm ABS dodecahedron, are fairly straightforward.
Next is an 8cm model of a hyperboloid of one sheet, showing how it is made of straight lines. (A version made from bamboo skewers was shown in this Math Monday column a year ago.)
And here is a tricky assembly puzzle made of twelve identical notched rods. They were dyed four different colors to help clarify the structure.
If you have access to a 3D printer, you can build your own copies of these models from the STL files available here.
See all of George Hart’s Math Monday columns