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4x4 algorithm

Feanaro

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Does anybody know an algorithm that will swap only two pieces on a 4x4? For example, on a solved american colour scheme cube it would be like swapping a blue yellow piece and a green white piece on the same slice. Thanks for your help.
 

Johannes91

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r U2 r U2 F2 r F2 l' U2 l U2 r2

Lower case means inner slice only. That swaps UFl and UBl (and also some centers, but I hope that doesn't matter).
 

MistArts

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Does anyone also know a move that will swap two face pieces on a 4x4 without messing up any other faces?

Do you mean Centers? Just set up for a 3-cycle. Like:

Lower case = slice

r l F' l b2 l' F l b2 l2 r'
 
A

andrewvo1324

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nevermind he was banned already. *talks about the spammer 2 posts aobve me*
 

cmhardw

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I think he meant two whole centres?
No I meant two individual center pieces. Is is possible to only swap two?

Yeah, practically during a solve use a 3-cycle to appear to swap 2 pieces.

You can actually swap just two centers on a 4x4, but you must also swap two corners to do so. On a 4x4x4 supercube the parity of the corners *must* match the parity of the x-centers.

Chris
 

blah

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@Chris: I don't quite get what you mean, does this mean that on a 4x4x4 supercube, the edges, centers and corners are not 'independent'? i.e. there's a possibility/probability that each 'piece type' cannot be solved by cycling 'within' itself?

Also, if there's an alg that swaps 2 center pieces and 2 corners, wouldn't it be more move-efficient to use this alg rather than solving the centers and corners independently? (which I think most people do, at least that's what I do...)
 

deadalnix

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On a normal cube, center can interchange if they are the same color. So you can do like you permute two center using a third of the same color and cycing 3.

It is the practical side of the thing (Sorry, i think i'm not very clear, but i'm not a native english speaker and i find this idea difficult to explain with my vocabulary).

Mathematicaly :

On a 333, when you rotate a face, you permute 4 corner and 4 edges. cycling pieces 3 by 3, you end with 2 corner and 2 edges to permute. On a megaminx, as you cycle 5 edges and 5 corner, you can't have parity ;)

On a 444/555, it's more complexe because you have two type of moves : a slice move and a face move. I will deal with 444, the idea is the same for 555.

A face move cycle 2*4 wing, 4 centers and 4 corners. A slice move 2*4 centers and 4 wings. The important thing is in the 2*4.

You can solve 2*4 cycle of the same type of pieces using standard 3-cycles. So a slice move generate a parity on wing and a face move generate a parity on corner and a parity on center.
 
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