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. 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. The main discussion group for all higher-dimensional puzzling is the 4D_Cubing Yahoo group. There has been quite a bit of discussion there regarding this puzzle, so look for conversations with "physical 2x2x2x2" in the subject. Feel free to join the group and ask questions.

How to get one


My friend Don Hatch and I came up with the idea for a virtual 4D Rubik's cube almost 30 years ago. I had the idea for the projection and UI, and he had the math chops to program the engine. I wrote all the code around his engine to produce MagicCube4D and have porting it from platform to platform over time ever since.

Almost from the beginning we and others in the community that grew around it wondered if one could ever make a 3D version of it. It's natural to want to touch it and operate it directly, but the physical requirements made that 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 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. 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 way to swap the outer axis with any of the other three, regardless of whether it used illegal moves since the sequence in total wouldn't affect the puzzle state. Eventually I found such a way, and then reduced it to a short enough sequence to be practical.

Then there was a final setback when I found that the magnetic arrangement wasn't quite good 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 ├╝ber nerds like myself! And of course I hope to be able to mass produce this someday. 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 to print your own which includes assembly instructions. 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 at a loss to as many people as I can afford to. If there is too much demand, then I will have to raise the price. The way to get the cheapest assembled puzzle will be to send me an email request for a quote. Put "2x2x2x2 quote request" in the subject line and I will attempt to respond to each request in the order that I get them with the lowest quote I can give you. You will eventually get the opportunity to accept it or not, and if you accept and pay for it, then you will get the next one. I have no idea how long the queue will get, but once it is your turn, you should get a puzzle within a month. I will also be happy to sign and number your puzzle if you like.


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 aggrement. If I die with 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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