Fred Hohman

3D Printing the Trefoil Knot and its Pages

At the University of Georgia I spent three semesters exploring 3D printing techniques in topology under Dr. David Gay in the Mathematics Department, in particular, visualizing complex shapes and knots using a MakerBot Replicator 2.

3D Printing the Trefoil Knot and its Pages.
My first designed, 3D printed trefoil knot.

My project involved programming, generating, and manipulating variations of the open-book decomposition of the complement of the trefoil knot in Mathematica to create a “3D printed puzzle” made of multiple pieces that hold together via small magnets.

During the summer of 2014, I was asked to guest post on Dr. Laura Taalman’s 3D printing blog MakerHome. She printed one object every day for a year, including my trefoil knot. I wrote a two-part piece for her website which described in detail the mathematical theory governing my research, the visualization techniques used, and models I had printed thus far. You can read the introduction here, part I here, and part II here.

I was then invited to repost this piece on Wolfram Community. At the end of 2014, the project spread around the internet and was written about by 3DPrint.com amongst other mathematics blogs, such as this Sketches of Topology post titled “Mathematics with 3D Printing.” Most recently, 3DPrint.com wrote a second piece about the completed project.

One of our users @fredhohman has written a great post about printing a 3D trefoil knot http://t.co/9J2YenPoRR pic.twitter.com/y63hxhT574

— Wolfram (@WolframResearch) December 5, 2014

Beautiful 3D prints of puzzles based on open-book trefoil knot decompositions by @fredhohman: http://t.co/amrWFoYRkI pic.twitter.com/x7gP3U5h2s

— Laura Taalman (@mathgrrl) August 27, 2015

Georgia Tech PhD Student Puts Finishing Touches on 3D Printed Trumpety Trefoil http://t.co/ChZzkoYxat pic.twitter.com/Tny3D2IxuA

— 3D Printing News (@My3DPrinting) September 12, 2015

Mathematics Student Creates 3D Printed Puzzle of Trefoil Knot, Gains Math Community’s Interest http://t.co/2rHMioiPjc pic.twitter.com/ux1FyJqPjl

— 3D Printing News (@My3DPrinting) December 6, 2014

Mathematics Student Creates 3D Printed Puzzle of Trefoil Knot, Gains Math Community’s Interest http://t.co/4l81gfN3Tk @thingiverse

— Eddie Krassenstein (@EddieKrassenste) December 5, 2014

After completing the project and 3D printing the final puzzle, I wrote my undergraduate thesis titled “3D Printing the Trefoil Knot and its Pages” and gave a talk at the 2015 UGA CURO Symposium.

3D Printing the Trefoil Knot and its Pages.
My UGA CURO Symposium Flyer.

I also took pictures of some of the configurations of the puzzle which can be seen below.

You can download my models from my Thingiverse profile to 3D print for yourself.

Features