Melinda's 2x2x2x2


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. There is also an active Hypercubers Discord server where speedsolving algorithms and related puzzles are being developed. Feel free to join the discussions.

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

16!×12^16/(6×192)

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 Rubik's original 33.


Erno
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.

History
How to get one
Where they went
Hall of Fame
License



History

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. It was somewhat affordable but eventually the cost of SLS printing rose to the point that few could afford it. I then needed to turn to injection molding to cut the price considerably. It took 3 years R&D but eventually I succeeded, and the result is far better than I hoped and at a fraction of the cost. 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'm thrilled to announce that I have succeeded in mass producing my puzzle! I had to learn all about injection molding and try a couple times to get a successful result. It took 3 full years, but the result is far better than I expected. It is much cheaper than the 3D printed version I had been selling, and it is simple enough for most people to assemble on their own. I am currently selling kits and fully-assembled puzzles. There is a long list of people waiting to buy, but if you send me an email and tell me what country you are in, I will add you to the list and tell you how to get updates. You can still have the old version printed on demand. I do not recommend that, but I have no reason to take away the option. And if you do buy the new version in kit form, here is an exploded view and an instructional video you can use to correctly assemble your cubies.

Where they went

map
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 hyperpuzzling!

Solutions
1
Bob Hearn
2017/11/22
First solution ever
2
Joel Karlsson
2017/12/21
3
Zander Bolgar
2017/12/31
4
Luna Peña
2018/1/20
Tutorial
5
Chris Harrison
2018/6/1
6
Joseph Cox
2018/6/16
7
Brian Pamandanan
2018/7/2
Turn captions on for annotations
8
Marc Ringuette
2018/7/12
9
Lucas Denhof
2018/7/24
7:24
10
Jay Berkenbilt
2018/7/29
Tutorial
11
Andy Farkas
2018/7/31
12
Will Dorrell
2018/9/17
13
Stephen McLeod
2019/5/16
14
Connor Lindsay
2019/8/11
15
Robert Mitchell
2020/2/5
16
Grant Staten
2020/5/9
World Record 1:07.57 on 2022/8/12
17
Yunqi Ouyang (欧阳韵奇)
2020/7/12
18
Jimmy Huguet
2020/9/18
12:31
19
Chetan Vashisht
2020/10/1
12:10 using Connor Lindsay's tutorial
20
Sara Sánchez
2020/10/26
Spanish tutorial and first from Spain
21
William Jestin Palmer
AKA Hyperespy
2021/10/10
22
Rowan Fortier
AKA Blobinati Cuber
1:28.14 on 2022/6/20
First Ever Sub-90 seconds
23
Ben Coppin
2021/11/18
24
Ann Malmsten
2021/11/26
25
Tim Szuba
2021/11/26
Neat double Sune at the end
26
Anie Garner
2022/5/23
27
Ty Jones
2022/5/30
28
Asa Kaplan
2022/7/14
29
Daniel Cohen
2022/7/15
30
David Brown
2022/7/27
31
Nicole Sheehan
2022/8/5

License

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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