Which Hypercube Unfoldings Tile Space?

UPDATE: The video has now been released! https://www.youtube.com/watch?v=Yq3P-LhlcQo Thanks for your help everyone.

Ok, there is a lot going on here! First of all: this is the very-rough cut of my next video. It is still missing a bunch of edits/transitions and all of the graphics. Please do not share it.

If you want to follow along with the maths, I’m basing much of it on this 1984 paper. You can see the sorts of diagrams etc I’m referring to. https://unfolding.apperceptual.com/

Any comments you have about the video: please do leave them in the, ah, comments below.

Next up: we need to both test WHUTS.org and recruit moderators. Anyone can submit a tiling or request to be a ‘verifier’ but we need a team of ‘moderators’ behind the scenes. Basically: the sad truth is that any open submission project on the internet is going to be abused. But I refuse to let that stop me! So we need a team of moderators prepared to confirm which submissions are legitimate. To be on the safe side: I am only going to recruit Patreon supporters as moderators. And this does not involve checking the maths at all: merely confirming the upload is a legit submission. This job runs a very high risk of seeing some NSFW stuff, so isn’t for everyone. I’m going to be in there doing my best to weed out all malicious submissions. If you’d like to join me, here is the secret sign-up link: https://whuts.org/register?patreon=2d47f0bf3791

And of course everyone can sign up to be a verifier or submit a tiling. I think it is only fair that you all get the first chance to find some of the tilings because without your support the project wouldn’t even be happening! Head over to https://whuts.org

If you have any issues with the site, either leave a comment below or email matt+whuts@standupmaths.com The site has been built by your fellow Patreon supporter Oliver!

AOB:

- I don’t have any plans to animate the ‘Dali cross’ net unfolding into 2D and then tiling a plane. But if anyone does: pop it in the comments! We’ll keep one comment thread dedicated to that so people are not duplicating effort.

- The Maths Gear link to buy the models is not live yet, but when it’s ready I’ll post it here first. UPDATE: https://mathsgear.co.uk/products/cube-model

- Please don’t leak the unannounced findings in the video.

- Sorry this video also has a sponsor message. Trying to keep everything afloat during the pandemic.

- Hope you enjoy the video!