Melinda's 2x2x2x2




This puzzle is a true 4D analog of the 2x2x2 Rubik's cube. I believe it is the world's first and only physical 3D embodiment of a 4D twisty puzzle. 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 group and ask questions. Note that we recently moved from Yahoo Groups because they stopped maintaining discussion history. Hopefully we can make that history visible somewhere else.

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 the 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. 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?

There are two ways. I can build one for you or you can have one printed and assemble it 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. I realize that that is still more expensive than many people can afford, so I am willing to build and sell completed puzzles for only my out-of-pocket costs to as many people as I can, so the way to get the cheapest assembled puzzle is to send me an email request for a quote.

Where they went

map
As of 2020/11/28

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!

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
World record 2:26 - Solution tutorial
15
Robert Mitchell
2020/2/5
16
Grant Staten
2020/5/9
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

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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