Pure dedge flip for supercubes (without disturbing centers)

[minime12358]

Pure dedge flip for supercubes (without disturbing centers)?

Hi, I was wondering if there is a pure dedge flip that I can use that does not mess with centers at all OR swaps them in a perpendicular to the dedge being flipped, so that you can do something like r parity r' without it messing up the centers. Sorry if there is a post somewhere about this, I couldnt find one.

 

[Christopher Mowla]

An algorithm that doesn't disturb centers only exists for the 4x4x4 and bandaged 4x4x4 even cubes. When translated correctly to higher order cubes (besides the case of bandaged 4x4x4 even cubes), it affects minimal centers. Here is one made by conjugating an opposite wing swap from TMOY:

r2 B2
U l U' l' U' l' U l U l' U' l' U' l D x' d2 l' d2 l x U D' (25 btm)
B2 r2

or if we shift the base algorithm and then conjugate, we have two half turn moves less:

x' r2 U2 l' U' l D x' d2 l' d2 l x U2 D' l U' l' U' l' U l U l' U r2 x (23 btm)

This can be optimized to:
x Rw2 U2 r U r' D' x' d2 r d2 r' x U2 D r' U r U r U' r' U' r U' Rw2 x'

You maybe interested in a pure 3-flip I made too:
M'2 U' r F2 (l' r) r U r l d2 l' r' U' r l Dw2 l' F2 l F2 D2 l F2 l' U2 r U' M'2 (28 btm for the 4x4x4)

But, to make things easier on yourself, just take your normal pure algorithm for nonsupercubes and do S before and S' after the algorithm (or vice versa), since you are just interested in doing r, r', l, l', etc. without messing up the centers. There are otherways to do this, but this is the easiest.