Message #4116

From: Marc Ringuette <ringuette@solarmirror.com>
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D cuboid
Date: Mon, 03 Sep 2018 11:35:39 -0700

CORRECTION – I mixed up some axes, so the best part of my last message
ended up quite scrambled.   I got all confused because the corner axes
of the regular and mini puzzle are named differently (R-L versus I-O).  
Here’s a better version of the comparison.

For the 2x2x2x2:    the short exchange of the U-D and corner (R-L) axes
is Iy Oy’, while the pure rotation, FOro, is Iy Oy’ Rx2 Bz2 Uy2 Rx2.  
The short half-exchange is Iy.
For the 2x2x2x1:    the short exchange of the U-D and corner (I-O) axes
is M y M, while the pure rotation, FRro, is  M y M R2 F2 R2 z2.  The
short half-exchange is M U M.

Note that I’m using a tweaked version of Luna’s gyro for the 2x2x2x1,
FRro, where I put the y rotation in between the restacks. This version
draws out the parallels between the 2x2x2x1 FRro and my favorite gyro
for the 2x2x2x2, ROIL FOro.  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.

Whatever the details, the parallel between these is still sweeeet.

–Marc

On 9/3/2018 10:22 AM, Marc Ringuette ringuette@solarmirror.com
[4D_Cubing] wrote:
> Here’s a different gyro for the 2x2x2x1, FUro, that corresponds
> (CORRECTION, NOT REALLY) to the mini version of my favorite gyro, the
> ROIL version of the FUro (CORRECTION, FOro) 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 (CORRECTION,
> U-D and L-R) axes is Iy Oy’, while the pure rotation, FUro
> (CORRECTION, FOro), 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.