# Message #4114

From: Luna Harran <scarecrowfish@gmail.com>

Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D cuboid

Date: Mon, 03 Sep 2018 18:52:22 +0100

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. 😉😁

~Luna

On Mon, 3 Sep 2018, 18:22 Marc Ringuette ringuette@solarmirror.com

[4D_Cubing], <4D_Cubing@yahoogroups.com> 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

>

>

>