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.

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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:





VisCAM View






Many other programs are available and may be useful:


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


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