About the Minimal Surface Archive


The purpose of this minimal surface archive is to provide information about important minimal surfaces. Ideally, each surface will be documented by

    • description of its properties
    • historical notes
    • high quality images
    • Movies showing animations
    • Mathematica notebooks exemplifying the meta code

This has been realized only to a limited extent so far. The limiting factors are time, the somewhat problematic stage of 3D graphics on the web, and a lack of an open platform to write mathematical software. Instead of detailing the problems, I will rather explain how the archive is being created.


Mathematica is used to prototype a library mesh.m of functions which are suitable to parametrize minimal surfaces, to create and manipulate 3D graphics, and to export the graphics into varies formats.

About 120+ notebooks build upon this library to create minimal surface models in a standardized way.

Currently, some 50 of these notebooks are publicly available, and more will follow.


The models are exported from Mathematica to POVRay and rendered. POVRay is hooked up with Mathematica so that it can also render animations. This currently only works in my development version of mesh.m.





The material in this archive is copyrighted, as is apparently everything else on this planet (and some other planets as well). In general, the pictures, models, and software on this web site may be used freely for purpoeses that are both educational and non-commercial. Please cite them properly.

Any other use requires my prior permission.

  If you are interested in high quality prints, please contact me. If there is enough interest, I will try to make the images available, provided I can find a suitable publisher. I have gatered print quality stereo pairs into a book, see the merchandise section.  

A final comment about the names of minimal surfaces. Commonly minimal surfaces have been assigned the names of the people who have discovered them. This has become very complicated. Not only are there at least a dozen (say) Hoffman surfaces, but in many cases the ownership is shared among many people: Somebody conjectured the surface might exist, somebody else wrote down a Weierstrass representation, a third person solved the period problem numerically, another one proved the existence, and yet another one proved that the surface is embedded. Instead of creating a nomenclature with five names and more for each surface, I have decided to use more descriptive names. An exception are those surfaces who are sufficiently classical. In short, the abuse of names ends here with the Costa surface.