Do you mean order cube? Because
@Tony Fisher has made cubes far larger than this. (Although I think his record was broken not to long ago. : (
Yes, of course. You cannot "hold" tony fisher's large 3x3x3 "in your hands", now can you? I guess I should have said nxnxn since most people may not be familiar with the phrase "cube size" being a synonym for "cube order".
it's true tho, 4x4 and 6x6 have pll parities beacuse its an even swap, but 5x5 doesnt because it's an odd swap, so that would be the same with a 32x32
People say you don't have to solve PLL parity on the 5x5x5 and larger odd cube sizes, but
what is this (specifically,
what algorithm did I use to generate that "edge pairing" case)? Isn't that one of the algorithms in
this list? Furthermore, people may want to argue that PLL parity can be when just two corners are swapped which "cannot happen on the 5x5x5", but look at what happens when I execute
this direct adjacent 2 corner swap algorithm (an alg that I found
partially by hand and partially with Cube Explorer) from
this list on the 5x5x5? (Doesn't it have a similar effect to how when PLL Parity is executed on a solved 5x5x5?)
Even though you're not "recognizing" PLL Parity on an even cube (typically -- I know some people know how to track PLL parity) until you finish the first 3 layers (or n-1 layers, in general) of a cube size n > 3 . . . but you can recognize it immediately after supposedly completely the tredges on the 5x5x5 . . . don't we call
this on the 4x4x4 and
this on the 5x5x5 the same thing? (And don't we solve them both with the same alg?) They are both the same
wing edge cycle. Just because it may look like two composite edges are swapped on the 4x4x4 with PLL parity (and just because it looks like one dedge is flipped on a 4x4x4), that's technically not the case if
you want to actually generalize the nxnxn. (In fact, I first mention that the one edge flip case is actually a single swap of wings in
my derivation of the red bull algorithm video.) PLL parity on
any cube size n > 3 is two separate 2 swaps (i.e. "2 2-cyle") of individual (i.e. "wing") edges.
If it walks like a duck (cannot be denied as being the same wing edge permutation) and quacks like a duck (the same algorithm can be used to solve it on both even and odd cube sizes), it must be a duck.