Message #3628

From: Ben Crabbe <>
Subject: Re: [MC4D] Physical 4D puzzle achieved
Date: Thu, 09 Feb 2017 10:48:53 +0000

Hi Melinda,

First of all thanks for sharing this great video. I am really excited about
the concept of a physical 4D cube of any size! The fact that you have a
working prototype is fantastic!

I have a few questions about rotations of the pieces. You never seem to
touch the outer two ‘rows’ of the cube, would this be an illegal move or
does the cube not allow it? Also could you rotate these two outer rows on
to the top of the cube? E.g. if row 1 was ‘rotated’ up on top of 2 and
likewise for 4 on top of 3? This would just seem to connect the grey face
pieces together from the looks of things. Furthermore, is there more legal
moves possible in the ‘flattened’ out form? Could the rows or columns be
rotated in various ways before ‘unflattening’?

I don’t have the 4D computer program with me right now so I can’t give

analogies to actual cube rotations but these are just the ideas that came
to me whilst I was watching your video.

I would be interested to hear from you regarding these questions.


Ben C

On 9 Feb 2017 09:10, "Melinda Green [4D_Cubing]" <> wrote:

> Hello Joel,
> That’s a great thought! Yes, the magnets allow that twist, and I had even
> considered that double end cap twist before prototyping, but forgot to
> analyze it afterwards. As you discovered, it’s definitely a valid 90 degree
> twist of non red-blue faces just like I asked. You are also correct that it
> doesn’t move red or blue stickers off that pair of faces, so it doesn’t
> solve the main problem but it is definitely a useful shortcut.
> Thanks!
> -Melinda
> On 2/9/2017 12:16 AM, Joel Karlsson [4D_Cubing]
> wrote:
> Hi Melinda,
> I just wanted to share a thought that I had when looking at the video. If
> you were to twist the two outmost layers of 2x2 pieces so that (if the

> magnets allow this) from 0:00 in your video, four of the light blue pieces
> would move down to the purple face. Wouldn’t this correspond to a legal
> 2x2x2x2 twist? To me, it seems like that would be a 90-degree twist around
> the gray face. This would not solve the problem of getting the reds and
> blues to other faces and, in fact, doesn’t add any permutations (I found a
> way to undo the twist with 10 twists of the types you showed in the video)
> but might work as a shortcut.
> Best regards,
> Joel Karlsson
> PS. The included picture shows such a move around the brown face.
> 2017-02-09 6:38 GMT+01:00 Melinda Green
> [4D_Cubing] <>:
>> Dear cubists,
>> I am excited to announce that I’ve been able to implement a working 2^4
>> in the real world! It uses a design I had described
>> <>
>> a little over a year ago. The key was a clever arrangement of magnets that
>> the Mathologer came up with for implementing a 2^3 puzzle. I realized that
>> it could be extended to give me a mechanism to support my design. I then
>> prototyped it and it works quite well. Here is a quick video I made just
>> for you:
>> Please do not share this link because it is unpublished and I intend to
>> delete and replace it with a proper video. It is mainly meant for getting
>> your feedback and advice. Please reply here, or privately to
>> if you’re shy. Feel free to comment on all
>> aspects of the video, and not just on the mathematics. For instance, feel
>> free to comment on the video and audio quality, or anything else that
>> strikes you.
>> Many of us have dreamed about such a puzzle for a long time and it’s
>> become something of a holy grail. It’s always seemed almost impossible to
>> create any sort of 4D puzzle in the real world, but there was never any
>> clear reason why it couldn’t be done. The real holy grail would be a
>> physical 3^4, so maybe this is just the baby grail. Of course maybe this
>> design can be extended to implement a 3^4. What do you think?
>> Happy puzzling!
>> -Melinda