I think it’ll still be impossible; it’s more of a mathematically impossible than a technically impossible. Why don’t you try it, you’ll see for yourself what I mean 
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Actually, maybe what @Gia suggests is possible, depending on how we define “left”. I think it could be defined analogously to shifting the longitude of coordinates on a globe by X degrees westward.
Pick two opposite faces of the cube and call them the top and bottom faces. You can consider the dead center of those faces as analogous to the north and south poles. Let’s also consider a cube made up of 4x4 faces, for ease of exposition, but it’s straightforward to generalize to other sizes.
For the top and bottom faces, one would rotate all of the points around the pole. That is, the four points in the center would rotate position, and the 12 points around the edge also rotate places. On the top face, this rotation would be one step in the clockwise direction, while on the bottom face, it would proceed counterclockwise.
For the rest of the four faces, they naturally form a ring, where each point would take one step “westward” (i.e. clockwise if viewed from the perspective of the top face) with points moving onto another face if already at the edge.
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I’m thinking how to make this IRL.
The OP one, I mean.
We could use magnetic stones. I have a portable set and at the club we have a big magnetic board with stones.
So a metallic cube would be good.
But what about holding it while playing?
Maybe something like a skewer?
With rests to hold it horizontally?
Or vertically maybe?
Or maybe something even more complicated, like a spherical cage?
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We could also use magnets to levitate the cube.
Or maybe just hang it from a string.
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What if the cube shrank one line after each move?
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What happens to the stones that might have been on it? Does the cube keep shrinking until it vanishes? What is the meaningful endgame and victory conditions?
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About the stones: the stones could just disappear and count for nothing, which could be an incentive to actually capture prisoners and not leave threatened groups. Or, all stones are automatically prisoners, based either on the edge after the shrinking or initial board edge.
About the size: it could shrink to a predetermined size, for example from 19x19 to 13x13, or any preagreed size really.
I’m still not sure about how to define endgame, but
Victory could be determined in the final size, and adding prisoners as per above.
Or victory is counted on the initial size, but corners and edges are less accessible as the board shrinks.
I accept any criticism, bar “this ruleset would be too complicated for Go”.
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I was in the process of making one from textile (or actually I did nothing more than order the supplies), but then I got the flu.
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Textile is a nice idea.
Something like velcro stones?
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I was thinking more like a pincushion
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Also felt should stick but is not so reliable, especially if you have to turn the cube in your hands to study your move.
For now I’m still wit tin and magnets:
This will be 5,5 cm wide.
Now I have to cut and glue and paint…
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This is the coolest idea I’ve heard for ages
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I like the orientation and I think I like the number of points too. The current 8x8x6 game with yebellz is doing my head in. 
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@Kosh How’s that game going?
It’s still going … EDIT: finished now
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It’s over and I think I’ve got PTGD (Post Traumatic Go Disorder).
In the opening I felt totally clueless. If anyone wants to recapture that feeling of what it felt like to be a beginner then this might be the way. I found it impossible to orientate myself and see the game as a whole. Gradually, very gradually it came together as the pieces themselves defined the board. For a significant part of the game I felt like I was playing “Puppy Go” though it might have been a case of two puppies chasing each other. 
yebellz scored a significant kill early on. (Dead Black stones still on the board uncaptured. Can you spot them?) Then followed some failed attempts at counter-attack by me, a desperate grab for anything that looked double-sente and a little reduction that probably shouldn’t have worked (not sure) at move 191.
Final result was B+Res with a probable score of around ~7 to 10pts. If there’s a bored, locked-down score estimating wiz out there, feel free. 
Summary: Cube-Go works. It really works and it really, really does your head in. I’m glad I did it but if I ever play again it will be 4x4x6 not 8x8x6.
Special thanks to @yebellz for being an awesome partner in the strange land of Cube-Go.
@Lys This image of yours reminds me of the movie, Contact. Very fitting.
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Looks very fun. I wouldn’t mind playing it. Though playing it on a flat board looks inconvenient, is it possible to make an intuitive coordinate system? And simply pm each other move coordinates?
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I think the answer to your question is ‘yes’ but what constitutes “intuitive” is very much going to depend on the participants.
The 8x8x6 was somewhat awkward and contrived but the arrangement for 4x4x6 was fairly straightforward.
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@Kosh, thank you for the game and the very unique and awesome experience.
It’s interesting to hear your perspective on the game. I think I was just as confused, but I felt that I was more of the puppy following you around too much. Regarding the early kill, it should also be noted that it was the product of some desperate fighting and out of sheer necessity to save one of my own groups that was under severe threat from @Kosh. And although I won that battle, I clearly lost the overall war, with not making enough efficient plays to secure territory on a larger scale.
@S_Alexander, I really feel that conveying moves through the flattened out board is actually the easiest way to do it. PMing coordinates could lead to errors, but looking at the image of the pieces of the board laid flat makes it very easy to locate and communicate moves. Further, as I mentioned above, there are a lot of other benefits to doing it via a game.
Perhaps the only suggestion is that I would make is to reduce the board size to 7x7 faces. This would make it a bit easier to fit within the largest game size available on OGS and it keeps the tradition of having odd dimensions. If OGS supported larger board sizes, 9x9 faces could be interesting to play with as well.
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