Message #4082

From: Jay Berkenbilt <>
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
[4D_Cubing] <> 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
> [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).