From Mathologer.

I’ve been meaning to make this video about building and solving physical 4D Rubik’s cubes ever since Melinda Green sent me one of her brilliant physical 2x2x2x2s back in 2017! Why did it take so long? Well, this one was especially tricky to get right, and I think it’s probably the video that took me the longest to put together. I really hope you like this one 🙂

00:00 Intro
03:53 Warm-up
08:59 4d
14:13 Fancy moves
20:24 Solve
26:20 Melinda
31:27 Coding challenge
31:46 What’s next?
33:54 Gallery of animations
36:10 Thank you !

Melinda’s 2x2x2x2 home page (go there straightaway !)
https://superliminal.com/cube/2x2x2x2/

Melinda’s YouTube page. Check out her 4D Twisty puzzle playlist.
https://www.youtube.com/c/melindagreen

Zasharan2 Melinda’s 2x2x2x2 simulator
https://zasharan2.github.io/2x2x2x2

A playlist of different ways to perform a gyro in Melinda’s puzzle

Joel Karlsson animation showing the correspondence between a different unfolded version of the real 2x2x2x2 and Melinda’s puzzle. https://www.youtube.com/watch?v=QvhkGRUeGco

Everything about higher-dimensional twisty puzzles
https://hypercubing.xyz

MagicCube4D is a fully functional four-dimensional analog of Rubik’s cube plus dozens of other beautiful 4D puzzles.
https://superliminal.com/cube/

Relevant Mathologer videos:
Cracking the 4D Rubik’s Cube with simple 3D tricks (solving the 3x3x3x3 in MagicCube4D)

Can you solve THE Klein Bottle Rubik’s cube?

A simple trick to design your own solutions for Rubik’s cubes

One of my Mathematica files—an animation of the hedgehog giro (.nb and .pdf)
https://www.qedcat.com/4dRubik

Hyperspeedcube, the name says it all
https://hypercubing.xyz/software/hyperspeedcube/

Piles of other simulators
https://hypercubing.xyz/software/

Grant Staten solves Melinda’s 2x2x2x2 in under a minute

The Unpopular Cuber solves the 3x3x3x3 using a simulator (the crazy action clip at the end of this video are a couple of seconds from this solve)

Some mathematical articles worth checking out:
The Rubik tesseract by H. J. Kamack and T. R. Keane
https://udel.edu/~tomkeane/RubikTesseract.pdf
Rubik’s Tesseract by Dan Velleman in Mathematics Magazine (1992), 65:1, 27-36. https://www.jstor.org/stable/2691357
n-dimensional sequential move puzzle https://en.wikipedia.org/wiki/N-dimensional_sequential_move_puzzle

Thank you very much to Melinda for all her help with this video. Also thank you to Vivian and Cristian from Monash’s FutureLab for their help with 3d printing the connectors that hold the cubies in my hedgehog together.

Music: Morning Mandolin by Chris Haugen

Enjoy!

Burkard