I was thinking to make classroom illustrations of some 3D mathematical objects, such as graphs of 2 variable functions, minimal surfaces, etc.

My question is, what would be a good way to go about it? I thought about 3D printers, but I have no experience with it whatsoever. I would really appreciate if someone with an experience with these things point me to a right direction.

  • 1
    $\begingroup$ 3D printing is maybe the most versatile and most expensive option but it becomes infeasible for things > 1dm^3. Which scales are you thinking about? $\endgroup$
    – Jasper
    Nov 21, 2018 at 7:12
  • $\begingroup$ Something that can be held by hand. 1dm^3 is I think exactly on the border. Sometimes, a bit bigger is preferred. $\endgroup$
    – timur
    Nov 21, 2018 at 13:58

4 Answers 4


Here are some examples of physical 3D-models of mathematical surfaces.
They might give you some ideas.

Of course, it's probably easy to find paper models of various solids (e.g. Paper Icosahedron, etc...) For example, https://www.korthalsaltes.com/


  • https://www.geogebra.org/3Dprinting
    3D Printing with GeoGebra by Diego Lieban
    "Create your own 3D shapes with GeoGebra and a 3D printer. In this tutorial you will learn how easy it is to export 3D constructions from our GeoGebra 3D Graphing app to the STL file format which can be printed directly on any 3D printer."

    It seems that it uses https://www.geogebra.org/3d and the STL output from the "Download as" menu item.

This is not what you are looking for, but I have had success explaining the Voronoi diagram and the medial axis by pouring dry sand. Here's an example of the medial axis. In (b) of the figure, one can discern a parabolic arc caused by the reflex vertex.

          Figure from Discrete and Computational Geometry.


It would help a little if you gave us some discussion of your limits in cost or time. The high cost, high quality approach is to buy models from vendors. If you can expense it go for it. The high quality (and you learn something), but also high effort and time, is to go into the machine shop (find one at your college or high school) and just mill something out of plastic or wood (metal not needed).

A happy medium would be to use sculpting clay and fire it. It will still be a fair amount of work, especially if you want it to look good.


If you have access to Rhino, you can develop 3D models and feed the model to a 3D printer. You can generate models using basic Python scripts here. I've done this with limited success. https://wiki.mcneel.com/rhino/3dprinting

In terms of basic 3D model rendering, I've also used VPython with Calculus students to make solids with known cross sections and solids of revolution. http://vpython.org/


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