#### tongjunhui

##### Member

Hi guys,

I'm looking for efficient nxnxn "atom" algorithms, here "atom" means a set of orthogonal algorithm with minimal possible "effect" on the cube. With these algorithms I can make any pattern on the cube (without breakout everything and build from bottom up).

For example, for 3x3x3 cube, the set of "atom" algorithms are:

- corner 3-cycle. (1 algorithm + conjugates => be able to loop any 3 corners)

- edge 3-cycle.

- corner swap + edge swap.

- flip 2 edges.

- rotate 2 corners by 120 degree.

- rotate 2 center pieces by 90 degree.

I will be very pleased if I can extend the above to nxnxn, my current progress are

- [done] 3-cycle of any pieces (corners, edge, centers, with the same kind) by: [aR' bD aR, U], where a and b are between 1 and n

- [done] flip 2 center edges (also by commutator, e.g. [R' E' R2 E2 R', U])

- [done] rotate 2 corners by 120 degree. (just like 3x3x3 does)

- [done] rotate 2 center pieces by 90 degree. (by [M' E M, U])

- [NEED HELP] swap 2 non-center edges with only one corresponding "+center" swap.

1. The traditional parity algorithm (2R2 B2 U2 ... one) on nxnxn has "(n-2)" additional center pieces swap: for even n, they are all unnecessary, for odd n, only one out of them (the "+center one") is necessary.

2. I extended the "super cube safe" 4x4x4 parity algorithm on wiki to 6x6x6 but a few arc center pieces affected suprisingly: https://alg.cubing.net/?alg=2R-_U-_2-3u_2R_U-_2R_U_2R_2-3u-_2R-_2-3u_2R_U_2R_U-_2R_U-_2-3u-_2R-_U2&puzzle=6x6x6

3. apparently I can do a (2R2 B2 U2 ...) one followed by several center pieces fix-up, e.g. (on 5x5x5) :

(2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2) (2B L' 2R' 2D 2R U' 2R' 2D' 2R U L 2B') y' (2B L' 2R' 2D 2R U' 2R' 2D' 2R U L 2B') y

but a big thinks if someone can provide shorter algorithms!

I'm looking for efficient nxnxn "atom" algorithms, here "atom" means a set of orthogonal algorithm with minimal possible "effect" on the cube. With these algorithms I can make any pattern on the cube (without breakout everything and build from bottom up).

For example, for 3x3x3 cube, the set of "atom" algorithms are:

- corner 3-cycle. (1 algorithm + conjugates => be able to loop any 3 corners)

- edge 3-cycle.

- corner swap + edge swap.

- flip 2 edges.

- rotate 2 corners by 120 degree.

- rotate 2 center pieces by 90 degree.

I will be very pleased if I can extend the above to nxnxn, my current progress are

- [done] 3-cycle of any pieces (corners, edge, centers, with the same kind) by: [aR' bD aR, U], where a and b are between 1 and n

- [done] flip 2 center edges (also by commutator, e.g. [R' E' R2 E2 R', U])

- [done] rotate 2 corners by 120 degree. (just like 3x3x3 does)

- [done] rotate 2 center pieces by 90 degree. (by [M' E M, U])

- [NEED HELP] swap 2 non-center edges with only one corresponding "+center" swap.

1. The traditional parity algorithm (2R2 B2 U2 ... one) on nxnxn has "(n-2)" additional center pieces swap: for even n, they are all unnecessary, for odd n, only one out of them (the "+center one") is necessary.

2. I extended the "super cube safe" 4x4x4 parity algorithm on wiki to 6x6x6 but a few arc center pieces affected suprisingly: https://alg.cubing.net/?alg=2R-_U-_2-3u_2R_U-_2R_U_2R_2-3u-_2R-_2-3u_2R_U_2R_U-_2R_U-_2-3u-_2R-_U2&puzzle=6x6x6

3. apparently I can do a (2R2 B2 U2 ...) one followed by several center pieces fix-up, e.g. (on 5x5x5) :

(2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2) (2B L' 2R' 2D 2R U' 2R' 2D' 2R U L 2B') y' (2B L' 2R' 2D 2R U' 2R' 2D' 2R U L 2B') y

but a big thinks if someone can provide shorter algorithms!

Last edited: Dec 27, 2021