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3D Printing the Trefoil Knot and its Pages

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This only includes introductory code. More advanced code coming at a later date (or available upon request)!

Exploring 3D Printing in Topology

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.

Here's the project page.

knot1

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.

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.

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.

Links

Gallery

knot2 knot3 knot4 knot5