Computational Geometry Research

The most most beautiful of things is math. I feel lucky to study it full-time at Stanford. Tadashi Tokieda, my advisor, is a big inspiration for the creative and wonderful mathematics he explores.

Numberphile, 3Blue1Brown, and Brady Haran's suite of channels saved my sanity during the pandemic. An idea clung on to me: could I find something myself? Naive me thought he could and took upon the challenge of extending the whuts.org project to higher dimensions.

I successfully did that for one case. I spent a lot of time chipping away, guided by intuition, Stack Exchange, and the rare email response from a professor. A year's time, spent on and off, and just in time for the JCCG deadline—with a guiding hand from Stefan Langerman—I crafted a high-speed algorithm that proved all the hypercube's unfoldings tile space, and those unfoldings can be unfolded to tile space. Beautiful?

Joseph O'Rourke, on the board of the conference, had previously done similar work where he showed this for one of the unfoldings using an algorithm that took 30 days. Mine computed 261 polycubes in one week. On a slow-ass laptop.

Conjecture, Stefan Langerman 2015: A polytope that monohedrally tiles ℝ^d is a c-DDT if all of its facet-unfoldings tile ℝ^d, and every polytope has a facet-unfolding that tiles ℝ^d-1. The polytope must then have a facet-unfolding that tiles ℝ^d-2 and so on till an edge-unfolding that tiles ℝ^d-1 polytope has a facet-unfolding that tiles ℝ^d-3. The polytope must then have a facet-unfolding that tiles ℝ^d-1 and so on till an edge-unfolding that tiles ℝ²

Conference Paper at Japan Conference on Discrete and Computational Geometry, Graphs, and Games JCDCG3 2022. At the time of publication, I was a 16 and belived to be the youngest author in the conference's history.