Message #4115

From: Luna Harran <>
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D cuboid
Date: Mon, 03 Sep 2018 19:13:33 +0100

Are these equivalent positions?

(M S R2 F2 R2 Y’ Z2 on physical puzzle)
(FRro’ UF2 IF2 UF2 on virtual puzzle)


On 3 Sep 2018 18:52, "Luna Harran" <> wrote:

Nice. I tried a while ago to get the 2x2x2x1 cuboid in MPU, but I can’t run
it at all at the moment unfortunately. Maybe someone with a better
understanding of the puzzle definition could try it out.

Also, could we perhaps find a way to simulate the 2x2x2x1 on the full 2^4?
That might help matters. I’m unsure quite what needs bandaging.

Could this also lead to a physical 3x3x3x1, or other such cuboids? Valid 4d
puzzles that are easier to construct.

Also, I’m a she. 😉😁


On Mon, 3 Sep 2018, 18:22 Marc Ringuette
[4D_Cubing], <> wrote:

> Hi gang,
> It’s becoming clearer to me that the mini-puzzle does indeed correspond to
> a 4D virtual puzzle, still not precisely defined, that is some flavor of
> 2x2x2x1 cuboid. As you’ll see by my discussion of gyro rotations below,
> the connection is looking pretty deep. In fact, I started messing around
> with the MC4D 2^4 hypercube puzzle (thinking of various colorings,
> projections, and allowed moves) in the hopes that I could figure out what
> 4D puzzle the mini-puzzle emulates. Can anyone see what it is yet? I’m
> not quite there.
> Gambling that this correspondence will pay off … I hereby name the
> mini-puzzle the 2x2x2x1 (or depending on context, "Melinda’s 2x2x2x1" or
> "the physical 2x2x2x1", but please never "Marc’s 2x2x2x1" because I prefer
> to stay under the radar, name-wise).
> My latest bit of insight was prompted by Luna’s discussion of the face
> swap versus the pure face swap:
> [ I will call M S the face swap.] The pure face swap is M S R2 F2 R2
> Y’. ~Luna
> The pure face swap that Luna describes looks just like a gyro rotation for
> the 2x2x2x1 ! (Actually, I might propose that a Z2 rotation be added to
> the end of his pure face swap, making it M S R2 F2 R2 Y’ Z2 , so that both
> the F-B and the L-R face pairs are completely unchanged. This is the 4
> dimensional "FR rotation", holding the F-B and R-L axes fixed while
> rotating the other two. So, this modified gyro for the 2x2x2x1 would
> sensibly be called FRro.
> Here’s a different gyro for the 2x2x2x1, FUro, that corresponds to the
> mini version of my favorite gyro, the ROIL version of the FUro gyro. The
> connection is deep enough that there are even three versions of each
> rotation: the short one on the physical puzzle, the longer one with
> cleanup moves to correspond to a one-click MC4D rotation, and the short
> half-exchange, that re-aligns only half of the puzzle corners.
> For the 2x2x2x2: the short exchange of the L-R and I-O axes is Iy Oy’,
> while the pure rotation, FUro, is Iy Oy’ Rx2 BO2 UO2 Rx2. The short
> half-exchange is Iy.
> For the 2x2x2x1: the short exchange of the L-R and I-O axes is E X E,
> while the pure rotation, FUro, is E X E F2 U2 F2 Y2. The short
> half-exchange is E R E.
> Sweeeeet.
> –Marc