Mathematical Impressions: Printing 3-D Models

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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:

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

 

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  • Hey George, great video, and thanks for showing Stella4D. Another (simpler) way you could make models for printing from Stella4D would be to display edges and vertices as cylinders and spheres. Then hide all the cells and export the model to your preferred 3D format.

    Enjoy,
    Rob.

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