# Mathematical Impressions: Printing 3-D Models

George Hart describes in this video how to create physical models of mathematical objects, surveying some examples of surfaces and polytopes.

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:

3DSurG

Stella

SeifertView

Mathematica

VisCAM View

netfabb

Rhino

Maya

Shapeways

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