Mathematics/Physics Student Creates 3D Printed Puzzle of Trefoil Knot, Catches Mathematical Community’s Interest


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Senior year of high school, I made room for drama in my class schedule by dropping from the track of honors math courses (Calculus? no, thanks!) I’d been taking since middle school. I went on to double-major in English and Theatre, which obviously my parents just loved. Since then, I’ve been working as an industry tech editor and writer for the better part of a decade, go figure.


But I’ve still never taken Calculus, so I’ll leave some of the finer points of this latest 3D print project to the mathematical experts who were behind it. As far as I’ve ever really been concerned, a trefoil is a Girl Scout cookie. Obviously, that isn’t all there is to it — a trefoil knot is a mathematically interesting prime knot whose mirror image is not equivalent. It’s a complicated three-crossing piece that proved to be a pretty intriguing project for a mathematics and physics student interested in 3D printing.

Fred Hohman

Fred Hohman

Fred Hohman recently came up with a 3D design for a puzzle of a trefoil knot and its fibrations that he could bring about via 3D printing. Hohman, who will graduate this coming May from the University of Georgia with his Bachelor’s degrees in Mathematics and Physics, had the chance to meet Dr. Laura Taalman this summer. Dr. Taalman is a respected mathematician with an interest in 3D printing, and the pair met following her presentation, “Making Mathematics Real: Knot Theory, Experimental Mathematics, and 3D Printing,” at MoMath. With Dr. Taalman’s encouragement, Hohman proceeded to create a code to render a trefoil knot in 3D using RegionPlot3D, which has a built-in Mathematica function.

Hohman went through a thorough process in Mathematica, in which he had to “specify the domain of valurenderes to plot over in the x, y, and z directions, as well as a mathematical inequality.” The piece involved several steps to render the design into 3D, sharing his process with the Wolfram community.

Through several steps of examples and iterations, Hohman presents the information needed not just to reprint his fully designed trefoil knot, but to allow users to create their own mathematical 3D printed masterpieces. His project has received some great attention from the mathematical community, including two guest blog posts on Dr. Taalman’s MakerHome blog and a feature on the Sketches of Topology blog post “Mathematics with 3D Printing.”

The finished design is now also available for download on Thingiverse, so you can print your own if you think the design is interesting, but maybe don’t quite want to design your own knot.


Hohman used Blender to create his 3D design, and a MakerBot Replicator 2 — courtesy of his professor, Dr. David Gay, at the University of Georgia  — to print the pieces. He also recommends Tinkercad if you’re interested in designing your own mathematically-inspired objects.

Check out the full story of Hohman’s creation, and let us know what you think about it over at the 3D Printed Trefoil Knot Puzzle forum at 3DPB .com.

trefoil render print

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