Holding the p-adics in the palm of your hand (with thanks to Matt Kukla)

A few years ago I made a picture of the 3-adic numbers in answer to a MathOverflow question (using the free 3d modeling and rendering software Blender, which I highly recommend despite its steep learning curve). Recently I discovered that I lost the original file, so I recreated it, with the following result:

View fullsize

Really this is \(\mathbb{Z}/243\mathbb{Z}\)

After I posted the picture above on Twitter, Matt Kukla, a budding mathematician and student at the University of Maryland, asked for the source file, and today, he’s posted a beautiful 3D print of the 3-adic numbers!

I've managed to 3D print @littmath's model of the 3-adic integers. The final product came out very nicely — a bit of fuzz on the upper prongs, but that should sand off easily.

Technically this is ℤ/243ℤ, but we've got a finite-filament printer... pic.twitter.com/uRatmHNV6U

— Matt Kukla (@n_category) February 12, 2019

EDIT 5/19/2019: If you’d like to try this yourself, here is the original .blend file and here is an exported .obj file.