Melinda's 2x2x2x2

This puzzle is a true 4D analog of the 2x2x2 Rubik's cube. I believe it is the world's first physical 3D embodiment of a 4D twisty puzzle. Specifically, the 24 The video above shows how it works, what the legal moves are, and the basic information you need to use it. A short follow-up video lists the set of canonial moves. For the mathematically curious, Marc Ringuette made a wonderful video showing the correspondence between the physical and virtual puzzles. The main discussion group for all higher-dimensional puzzling is the hypercubing Google group. Feel free to join the discussions.

The number of possible states for the 4D cube is exactly


or in decimal as
3 357 894 533 384 932 272 635 904 000

This means the 24 has about a billion times as many states than the original 33.

Ernő Rubik examines the puzzle

Above is professor Rubik himself examining one of my puzzles at the 13th Gathering For Gardner conference. It was reported that his only comment was that none of the derivative puzzles matter and that only his original invention is important.

How to get one
Where they went
Hall of Fame


My friend Don Hatch and I came up with the idea for a virtual 4D Rubik's cube almost 30 years ago. We then wrote the first version of MagicCube4D and have porting it from platform to platform ever since.

Almost from the beginning we and others in the community that grew around it wondered if one could ever make a physical version of it. It's natural to want to reach in to touch it and operate it directly, but the physical requirements made a physical version seem incredibly unlikely. Still, I could never completely stop thinking about that. Deciding to focus on a 24 rather than the full 34 was helpful but still there was no clear way to achieve even that.

In early 2014 I was discussing this with Oskar van Deventer and I sent him some rough sketches of the pieces and topology involved. He turned that into a beautiful rendering though neither of us had any idea for a mechanism that would allow it to function. The rendering was very inspirational however and I kept coming back to it. Eventually I had the idea of stretching it into a less symmetrical configuration and squashing the pieces into cubes.

At that point I seemed to have a design for a potentially workable puzzle but still had no idea for a mechanism. I figured that magnets were probably my only hope but how to do that was far from clear. Around the end of 2016 I stumbled onto a Mathologer video about magnetic Rubik's cubes made from dice. It included a magnetic arrangement that allowed for a workable 23 and I realized it might be extended to do what I needed. I built my first prototype and thought I may have accomplished it.

Then we discovered that it wasn't exercising the full state space of the 4D puzzle and that was a big setback. Eventually I realized that I could reach the full state space if I could just find a kind of 4D rotation that would swap the outer axis with any of the other three. Eventually I found such a way and reduced it to a short enough sequence to be practical. We came to call this a "gyro" move.

Then there was a final setback when I found that the magnetic arrangement wasn't quite general enough to support such a transformation, but Matthew Sheerin quickly realized that that could be fixed at the expense of doubling the number of magnets to 384. That's a lot of magnets, but who cares about that if it works!

This was when I needed to move to 3D printing, so there was a lot of learning and experimenting to make a printable design at any kind of reasonable price. I know that few can afford the cost of SLS printing, but at least a true physical 4D twisty puzzle finally exists, and that makes it a must-have for a certain class of über nerds like myself! I am currently working to have it injection molded to cut the price considerably. I still think it's a kind of a miracle that this all came together after so very long.

I must have this! How can I get one?

I had been selling these for my cost, but the 3D printing costs have gone up so much that I feel bad, so I've been working hard to get the parts mass produced to drastically lower the cost and improve quality. I am making good progress, so I encourage you wait. send me an email and I will add you to a list of some of the first people who can buy them. And if you simply can't wait, I'll still let you print and assemble one yourself. This is the page where you can have one printed on demand and where you will find instructions to assemble it yourself. Note: You need to buy all 8 colors, not just one! It is currently set at the minimum possible price, meaning zero mark-up for me. Here is an exploded view of the cubies you can use to correctly assemble your cubies.

Where they went

As of 2021/10/28

Hall of Fame

Here are all the accepted solutions to this puzzle. If you solve it and would like to see your name listed here, simply shoot a video of yourself, upload it to YouTube, and send the link to the address above. You can make it unlisted if you don't want to share it publicly. If you do share it publicly, I will link your name to your solution. Your video doesn't need to be anything fancy. Simply propping up your cell phone is perfectly fine. It just needs to be in one long, unedited shot from scrambling to solved, using only canonical moves, and with the puzzle in the frame the whole time. Ideally you would also talk us through your solution, but that's optional. You can develop your own solution or learn from others below. Note that some of the early solutions were done before we settled on a cononical move set. Some of them are difficult to follow, and some are very good tutorials. Happy puzzling!

Bob Hearn
First solution ever
Joel Karlsson
Zander Bolgar
Luna Peña
Chris Harrison
Joseph Cox
Brian Pamandanan
Turn captions on for annotations
Marc Ringuette
Lucas Denhof
Jay Berkenbilt
Andy Farkas
Will Dorrell
Stephen McLeod
Connor Lindsay
Robert Mitchell
Grant Staten
Yunqi Ouyang (欧阳韵奇)
Jimmy Huguet
Chetan Vashisht
12:10 using Connor Lindsay's tutorial
Sara Sánchez
Spanish tutorial and first from Spain
William Jestin Palmer
AKA Hyperespy
Rowan Fortier
AKA Blobinati Cuber
World Record 1:28.14 on 2022/6/20
First Ever Sub-90 seconds
Ben Coppin
Ann Malmsten
Tim Szuba
Neat double Sune at the end
Anie Garner
Ty Jones


Copyright (c), Melinda Green, Superliminal Software. My intention is for this design to enter the public domain upon my death, though I reserve ownership and control until then. So please do not copy, steal, or reproduce it in any way before then without my written agreement. If I die while this notice is still in place, then you have my permission to do what you like with it, even if someone else claims ownership. Just please keep my name attached. Sound fair?

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