How many 3D nets does a 4D hypercube have?

Опубликовано: 22 Октябрь 2024
на канале: Stand-up Maths

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Which hypercube unfoldings tile space? https://whuts.org/

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. https://mathsgear.co.uk/products/cube...

Here is Giovanna Diaz and Joseph O’Rourke's paper: https://arxiv.org/abs/1512.02086

A091159 Number of distinct nets for the n-hypercube. https://oeis.org/A091159
The code Moritz used to find these values is here: https://github.com/google-research/go...

All of Moritz Firsching's 3D models: https://mo271.github.io/mo/198722/unf...

Their post on the number of unfoldings in higher dimensions. https://mathoverflow.net/questions/30...

This is the Math Overflow post which started it all: https://mathoverflow.net/questions/30...

Peter Turney's 1984 paper Unfolding the Tesseract https://unfolding.apperceptual.com/

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: https://amzn.to/3bsWOZd
UK: https://amzn.to/3offAsr

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 whuts.org site. Thanks so much for all of your help everyone! / 51144440

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. https://creativecommons.org/licenses/...
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Artist: http://incompetech.com/
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MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
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