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

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.

haiii.. its a grate video…how make stl file from SeifertView.

Don’t know if you guys have seen this yet, but there’s a playlist here of some incredible mathematical modeling tutorials, for free. The cool thing is that these techniques can be done with any standard polygon modelling software, and no need for knowledge of complex formula.

https://youtu.be/0cogrpgJ6S0?list=PL95vjV728MLdFVM4e9z0x2vN2Tf7McT9m

I m interested in using 3d printing to illustrate mathematical lessons to high school students. Any suggestions of how I can hold of printers, software ,other needed matrials and how to print.

Eli, in addition to the links provided above, further relevant information is provided at George Hart’s Rapid Prototyping page.

The National Musum of Mathematics has held “Introduction to 3D Printing” workshops in the past (1, 2); you may wish to check their events page occasionally to see if they announce more.

Resources and further Ideas for mathematical concepts that can be illustrated with 3D printing can also be found on sites like:

http://3dmathmodels.site.wesleyan.edu/category/resources/

http://www.ms.unimelb.edu.au/~segerman/papers/3d_printed_visualisation.pdf

https://plus.maths.org/content/3d-printing

http://mathgrrl.com/hacktastic/

http://sdu.ictp.it/3D/book.html