Get to know Jane Street! Which hypercube unfoldings tile space? Yes, you can buy one of the 261 models from this video and support the channel. All hand-numbered by me and with a signed certificate of authenticity. Here is Giovanna Diaz and Joseph O’Rourke's paper: A091159 Number of distinct nets for the n-hypercube. The code Moritz used to find these values is here: All of Moritz Firsching's 3D models: Their post on the number of unfoldings in higher dimensions. This is the Math Overflow post which started it all: Peter Turney's 1984 paper Unfolding the Tesseract The cubes I am using are called "mathlink" and I just bought a huge quantity from Amazon (because Learning Resources didn't answer my emails). US: UK: The unfolding animation of the 'Dali cross' was kindly made by my Patreon supporter John Sawyer. I actually put the rough-cut of this video out on Patreon earlier this week so they could provide feedback and help test the site. Thanks so much for all of your help everyone! CORRECTIONS: - I saw "288" at the end of the 8D number when it should be "228". The on-screen number is correct. I noticed too late to fix it! - At 21:09 I say Diaz and O’Rourke found an unfolding of the Dali cross which tiles the plane. It’s actually a different 3D net they found which does this and the Dali is undetermined if it produces a tiling 2D net. (Thanks Dan L by email.) - Let me know if you spot any more mistakes! Filming and editing by Alex Genn-Bash Maths graphics by Matt Parker Music by Howard Carter The song Hep Cats by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. Source: Artist: Yeah, I decided to replace the copyright-claimed Aerosmith. Design by Simon Wright and Adam Robinson MATT PARKER: Stand-up Mathematician Website: US book: UK book: