7x7 cube with the reduction method - cheat sheet

Reduction method: centres (6 piece types), edges (inner, then outer wings), as a 3x3. Full course with animations and simulator: strefa-kostek.pl/en/kursy

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1Move notation

R U F… - one outer layer, a quarter turn clockwise, looking at that face. 2R / 3R = only the second / third layer from the right, 4R = the middle layer (direction as R), Uw = two layers, 3Uw 3Rw = three layers. Order: centres → inner wings (as 5x5, 3Uw) → outer wings (as 5x5, Uw) → as 3x3, no parity in the 3x3 part. Face colour = its fixed centre.

2Centres: 6 piece types (from the front to the top)

Left diagram: top (back at the top), right: front; yellow = the colour being built. Turn F so the piece is in the circle, and U so the spot in the circle is free. The algorithm changes only that spot on top.

corner2R U 2R' U 2R U2 2R'

inner corner3R U 3R' U 3R U2 3R'

outer arm2R U 4R U' 2R' U 4R' U'

inner arm3R U 4R U' 3R' U 4R' U'

side, higher2R U 3R U' 2R' U 3R' U'

side, lower2R U' 3R U 2R' U' 3R' U

3Rw' D2 3Rw two left columns of the bottom ↔ two right columns of the front (from the bottom to the front; only while the bottom is not solved). Another side face to the front: y.

3Order (as 5x5)

White fixed centre on top.
x2, yellow - no moves from the bottom.
z: white on the left, yellow on the right. Rotations only x and y2.
Ring: from the front, from the bottom, from the back (y2).
x, the next one: from the front and from the bottom.
x, the next one only from the front - the last one solves itself.
Then as 3x3 (yellow on top, outer moves only, no parity).

4Inner wings

Wing at front right, front = colour of the middle piece on the left (otherwise R U R' F R' F' R).
At the bottom: 3Uw' R U R' F R' F' R 3Uw
At the top: 3Dw R U R' F R' F' R 3Dw'

Last edge (colour, other, colour, other, colour), at top front:

3R2 B2 U2 3L U2 3R' U2 3R U2 F2 3R F2 3L' B2 3R2

5Outer wings

Triple = the middle piece of the 5x5.

At the bottom: Uw' R U R' F R' F' R Uw
At the top: Dw R U R' F R' F' R Dw'

Last edge (other, three correct, other):

2R2 B2 U2 2L U2 2R' U2 2R U2 F2 2R F2 2L' B2 2R2

Only Uw / Dw (two layers). The right edge must not be a finished one.

9+Bigger odd cubes

Piece in the right half: column = layer a, row = b. a≠b: aR U bR U' aR' U bR' U' (lower half: U↔U'), free spot in the same place. a=b: aR U aR' U aR U2 aR'.
From the bottom: kRw' D2 kRw, k=(N-1)/2.
Wings from the inside out: kUw / kDw, parity with kR.

!When something goes wrong

Piece does not go in: free spot of a different type - check the circles in point 2.
Fixed centres moved: an interrupted algorithm with 4R.
Triples fell apart: in step 5 only Uw and Dw.

Letter = quarter turn clockwise, looking at that face; ' = the other way; 2 = half turn. 2R / 3R = only the second / third layer from the right, 4R = the middle layer (direction as R), Uw = the two top layers, 3Uw / 3Rw = three layers. StrefaKostek.pl