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3D Printing the Trefoil Knot and its Pages

Posted 4 years ago
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Who are you?

Hello Wolfram Community! I’m Fred Hohman, a Ph.D. student at Georgia Tech studying Computational Science and Engineering in the College of Computing. However, I recently graduated from the University of Georgia where I worked with Dr. David Gay in the Department of Mathematics on a project exploring topology via 3D printing.

What about this 3D printing thing?

This project spanned my last three semester at UGA and I wrote my undergraduate thesis covering most of the mathematical and computational details of the project.

The project involved programming, generating, and manipulating variations of the open-book decomposition of the complement of the trefoil knot in Mathematica to create multiple pieces that hold together via small magnets so that one could physically build a 3D puzzle.

I used Mathematica exclusively to generate the unedited 3D models of the trefoil knot and its pages.

Didn't you already post here before?

When I was about halfway through the project I posted my preliminary results here on Wolfram Community and was met with interest. So here I am again, but this time with a completed project and a gallery of pictures showcasing the final model in its various configurations.

Pictures, Math, and Links

A few of the pictures of the model can be seen in this Wolfram Community post, but I have many more in a gallery here. If you want to read about the specific mathematics and computations used in this project you can read my entire undergraduate thesis here (also attached to this post). Finally, I have some .stl models posted on my Thingiverse profile that anyone can download and print for themselves!



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