Six color 3x3 barrel cube parity

[Eelephant]

hello, all, need to solve pll parity on a six color barrel. The only algs I can find are for 10 color... if I understand correctly, these algs switch the entire column, which is fine for a 10 color, but in a six color, you are taking that column away from its sister (same color) column. Dig? I'm using a 10 color oll alg to solve the oll parity in the 6 color, cuz it happens to work in both, but the pll alg doesn't work on the 6 color, as near as I can tell...

Any help?

 

[xyzzy]

Not 100% sure what your parity situation is (pictures would help!), but I think what you need to do is to match the "columns" with the other side of the centres, e.g. like (L' U F' U2 F U' L) (L R U2 L' R') (F' U R' U2 R U' F).

 

[Eelephant]

Not 100% sure what your parity situation is (pictures would help!), but I think what you need to do is to match the "columns" with the other side of the centres, e.g. like (L' U F' U2 F U' L) (L R U2 L' R') (F' U R' U2 R U' F).

Hey, man, thanks for the help. It's the same parity situation you get on a 4x4. Not the edge flip/cross error, but the corner swap one. Where after running (U R U' L') (U R' U' L) a couple times, it becomes clear that two of the last corners will never match up.

So, like I said, I tried an alg that appears to be for a ten color, where you basically switch the entire column (instead of just the top edge pieces), and deal with it that way. So, I did that, permuted the last layer pieces, then tried to flip the columns back to where they should be. Succeeded in that, but it messed up the top cross edges and such. So, fixed everything that column switching messed up, and lo and behold, corner swap parity has reappeared. I think I uploaded a picture, we shall see if it worked. Basically, the red "corner" piece needs to be swapped with the orange "corner" piece opposite it.

Thanks again for the help.

 

[xyzzy]

So, like I said, I tried an alg that appears to be for a ten color, where you basically switch the entire column (instead of just the top edge pieces), and deal with it that way.

You need to cycle all four columns, rather than switching only two columns. The alg I posted before, (L' U F' U2 F U' L) (L R U2 L' R') (F' U R' U2 R U' F), does exactly that, although you'll still need to fix the last layer after that.

Spoiler: why this works and what is going on, if you're curious (so you can solve other puzzles on your own)

Holding yellow on top, it looks like you could solve the orange column to the right of the orange centre, the green column to the right of the green centre, and so on; or you could solve the orange column to the left of the orange centre, the green column to the left of the green centre, and so on. However, these two solved states have different permutation parity: you cannot go from the "columns left of matching centres" solved state to the "columns right of matching centres" solved state. The reason for this is that they differ by two 4-cycles on the corners and a 4-cycle on the edges, which is an odd permutation.

In this case, after you've tried solving most of it to "columns right of matching centres", you've found that you need to swap just two pieces, which is an odd permutation. In other words, "columns right of matching centres" was the wrong guess, and "columns left of matching centres" is the only attainable solved state on your puzzle. (Unless you disassemble and reassemble it into the other one, of course.)

 

[Eelephant]

You need to cycle all four columns, rather than switching only two columns. The alg I posted before, (L' U F' U2 F U' L) (L R U2 L' R') (F' U R' U2 R U' F), does exactly that, although you'll still need to fix the last layer after that.

Spoiler: why this works and what is going on, if you're curious (so you can solve other puzzles on your own)

Holding yellow on top, it looks like you could solve the orange column to the right of the orange centre, the green column to the right of the green centre, and so on; or you could solve the orange column to the left of the orange centre, the green column to the left of the green centre, and so on. However, these two solved states have different permutation parity: you cannot go from the "columns left of matching centres" solved state to the "columns right of matching centres" solved state. The reason for this is that they differ by two 4-cycles on the corners and a 4-cycle on the edges, which is an odd permutation.

In this case, after you've tried solving most of it to "columns right of matching centres", you've found that you need to swap just two pieces, which is an odd permutation. In other words, "columns right of matching centres" was the wrong guess, and "columns left of matching centres" is the only attainable solved state on your puzzle. (Unless you disassemble and reassemble it into the other one, of course.)

Holy cow, yup, I just looked at the marketing picture of the solved cube, and see that the columns are to the LEFT of matching centers, and I am trying to solve them to the right. Armed with that knowledge, I'll try to tackle this again. Thanks!

Oh, man, do I feel stupid. I was trying all along to literally solve it incorrectly. Thanks a lot, my friend.