# Mathematical Impressions: Printing 3-D Models

It’s getting easier to make physical models of mathematical objects. This video surveys some examples of surfaces and polytope models. A variety of software packages are used to create a description of the geometry (an “stl file”), which is then sent to a 3-D printer to be fabricated. The software used for these models is:

Many other programs are available and may be useful:

http://reprap.org/wiki/Useful_Software_Packages

http://www.shapeways.com/tutorials/supported-applications

The 3-D printer shown is a Replicator.

Tori parametrically defined as 0 < u < 2Pi, 0 < v < 2Pi:

*x* = (3 + cos(*v*)) * sin(*u*)

*y* = (3 + cos(*v*)) * cos(*u*)

*z* = sin(*v*)

*x* = (3 + 0.2 * cos(20 * *u*) + cos(*v*)) * sin(*u*)

*y* = (3 + 0.2 * cos(20 * *u*) + cos(*v*)) * cos(*u*)

*z* = sin(*v*)

Triply periodic surface:

cos(*x*) + cos(*y*) + cos(*z*) + 3/2 cos(*x*)cos(*y*)cos(*z*) = 0