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Math Monday: 3D Hilbert Curve from plumbing supplies

By George Hart for the Museum of Mathematics

The 3D Hilbert curve is an infinitely long path which wiggles around through all regions of a cube, making right angles in a systematic manner.


Physical models can be made with additive fabrication technology. The elegant metal version above was designed by Carlo Séquin. If you have access to a fabrication machine, you can try making your own using the .STL files that Carlo has provided here.


Chaim Goodman-Strauss had the idea of making a large version from plumbing supplies. The above construction uses sixty-four PVC elbows.


Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.



  1. Sean Michael Ragan says:

    This is one of my favorite features we’ve ever run, and this post in particular is awesome. I cannot get enough geometric and/or topological curiosities.

  2. says:

    Now I want to make an sgi logo:

  3. ruzter says:

    Hilbert Curves make great designs for decorative projects where you want to fill a space. I use them on my CNC trivets.

  4. craig says:

    So YOU’RE the guy who is putting the street 90s together in the bin at Home Depot! I need one street elbow and have to spend 5 minutes wrestling them apart! 8^)

  5. A good buyer always inquires, how much, but the wise buyer always asks, how less. Discount is such a sweet word for any consumer. The more we can haggle products, the better; and if we get to grab a discount plumbing supplies for keeps, then we’d almost feel our ears flapping with joy.

    1. Nicely put but honestly have you read the article?

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