# Message #4082

From: Jay Berkenbilt <ejb@ql.org>

Subject: Re: [MC4D] 2x2x2x2: List of useful algorithms (please add yours)

Date: Mon, 30 Jul 2018 18:34:46 -0400

I’m rejoining discussions after a long break. Can you point me to some post

where you introduce your notation? I can more or less figure it out, but

I’m curious to see whether you described it somewhere. I came up with my

own notation during my independent work, and it seems very similar to

yours. I haven’t posted mine anywhere since I figured I’d wait and see

whether a standard notation had been agreed upon by the list first.

On Sun, Jul 29, 2018 at 3:04 PM Marc Ringuette ringuette@solarmirror.com

[4D_Cubing] <4D_Cubing@yahoogroups.com> wrote:

>

>

> I thought I’d re-read Joel Karlsson’s message from 12/21/2017 discussing

> the commutators that he used to solve the puzzle, and pondering it led

> me to this nice short double pair swap.

>

> 2x2 cycle: Uy2 Lx’ Uy2 Lx Uy2 Rxy2 Uy2 Lx’ Uy2 Lx Uy2 Rxy2 (12

> moves canonical)

> (all changes are in the UF quarter of the puzzle, LUFO <–> LUFI,

> RUFO <–> RUFI)

>

> And a related 3-cycle,

>

> 3-cycle: Uy2 Rx’ Uy2 Rx’y2 Uy2 Rx Uy2 Ly Uy2 Rx’ Uy2 Rx’y2 Uy2 Rx

> Uy2 Ly’ (16 moves canonical)

> (all changes are in the LU quarter of the puzzle, LUFO –> LUBI –> LUBO)

>

> Both of these act on a restricted 1/4 of the puzzle, in contrast to the

> 3-cycle I gave in yesterday’s list, where the pieces involved are widely

> distributed around the puzzle, so that there is no half of the puzzle

> that does not contain a moved piece.

>

> 3-cycle: Lz’ Fz2 Lx Fz2 Lx’ Fz2 Lz Ox2 Lz’ Fz2 Lx Fz2 Lx’ Fz2 Lz

> Ox2 (16 moves canonical)

> (moves LUFI –> RUFO –> RDBO)

>

> Hmm, I wonder if there might be a sensible classification scheme for

> cycles and swaps based on the number of dimensions that are twisted, the

> number of half-puzzles that are unchanged, and the fraction of the

> orientations that can be accessed. At this point I have no idea.. As I

> try to develop an efficient 3-cycle-based solution scheme, maybe it’ll

> come to me.

>

> On 12/21/2017 2:05 PM, Joel Karlsson joelkarlsson97@gmail.com

> [4D_Cubing] wrote:

> > The commutators I use are based on one simple idea. Isolate one or two

> > pieces (depending on what you want to accomplish) from the bottom half

> > on the top half (holding the cube upright), then rotate the top face

> > (to accomplish a swap or rotation for example), reverse the first

> > step, rotate the bottom face and lastly perform the first three steps

> > in reverse. The first step can quite easily be done with 7 and 3 moves

> > respectively, resulting in sequences from 7 to 32 moves (sometimes the

> > first three steps are enough, depending on how much you want to

> > preserve).

>

>