This document provides notation for solving a 5x5x5 Rubik's cube. It describes:
1) The parts of the cube including the 6 faces with 25 stickers each, 6 centers with 9 stickers, 12 edges with 2 stickers each, and 8 corners with 3 stickers each.
2) Inner layers that are named the same as faces in lowercase except for M, E, and S layers which remain uppercase.
3) A matrix notation using rows and columns to specify positions of individual pieces within each face like (1,1) for top right.
4) Notation for turns and rotations including letters for clockwise outer layer turns, lowercase letters for inner layers, brackets for
2. 1 Parts of the cube
1.1 Faces
Faces are the plane surfaces that contain 25 stickers. There are 6 faces.
Figure 1: English notation of faces.
1.2 Centres, edges and corners
Centres Edges Corners
For us, centres are not the central
pieces of each face, but the central
3x3-sticker surfaces that de鍖ne the
colour of every face. There are 6
centres, with 9 stickers each.
Likewise, we call edge to the
three-piece group, with two stickers
each. There are 12 edges in the
cube.
Corners are the pieces containing 3
stickers. There are 8 corners.
1.3 Inner layers
They are named the same way as the faces but with lower case letters (except for M, E y S layers, which are upper
case because there can be no confusion with other layers).
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3. Table 1: English notation of inner layers
2 Matrix notation
To simplify the understanding of certain algorithms, we use a matrix notation to point the position of a given piece in
a given face. Said position is indicated by its row and its column, like this:
Piece position = (row, column)
Example: The piece located in the top right position is the (1,1); that means it is in row 1, column 1. Likewise, the
piece located in row 3, column 2 is the piece called (3,2).
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5)
Figure 2: Scheme of matrix notation.
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4. 3 Turns and rotations of the whole cube
In the following pictures, red arrows inicate clockwise turns and blue arrows indicate counterclockwise turns.
Turns of outer layers Turns of inner layers Turns of inner and outer layers at
same time
To indicate a clockwise turn, the
letter of the face is written.
Example: R
To indicate a clockwise turn, the
letter of the face and an apostrophe
are written.
Example: R
To indicate a double turn, the letter
of the face and a number 2 are
written.
Example: R2
The turns of inner layers are
indicated just like the outer layers,
but using lower case letters.
Examples:
Clockwise turn: r
Counterclockwise turn: r
Double turn (180
): r2
We can also turn both the inner and
the outer layer at the same time;
this is indicated with the upper case
and the lower case letters in
brackets. Examples:
Clockwise turn: (Rr)
Counterclockwise turn: (Rr)
Double turn (180
): (Rr)2
As for the rotations of the whole cube, they are indicated with letters x, y and z as follows:
Just the letter if it is a clockwise turn.
Example: x
The letter and an apostrophe if it is a counterclockwise turn.
Example: z
The letter and a number 2 if it is a double turn.
Example: y2
Figure 3: Rotations of the whole cube.
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