Message #3851

Subject: Re: Cuboid parity-esque situation on a {6}x{4} duoprism
Date: Sat, 02 Dec 2017 21:33:27 +0000

I didn’t solve this, but I have a feeling that there is no "swap two pieces" algorithm, only "cycle 3 pieces". "swap two pairs" is actually "cycle 3" two times… The biggest issue I see is that you have a single 2-color problem and a single 3-color problem while everything else is done, 4-color pieces included! My solving methods don’t allow me to solve this without destroying the rest of the cube, lol.:D

My gut tells me that this parity issue can probably only be solved by doing a twist of the middle hex face.
This will make the whole thing have only 1 two-color piece in place and 5 two-color pieces not-in place, then you can solve those five by doing 3-cycle algorithms.
This will screw up all the 3-color and 4-color pieces as well!

…and that’s only for two color pieces, the 3 color parity might be solved by this, it might not…

I did some "test work", files attached