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Rubik's Cube theory

Basic definitions

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Pieces

If you take your Rubik's cube apart, you will find that it is made from 21 separate pieces:

12 edge pieces, each having 2 sides,

8 corner pieces, each having 3 sides,

And finally, 1 centre piece, having 6 sides.

Orientation

Orientation refers to the act of twisting pieces to face in a certain direction, regardless of their location. Orientation may also refer to the actual direction itself. The following sequence orients the 4 top corners so that the white sticker of each piece faces upwards.

Permutation

Permutation is the act of rearranging the pieces on a cube. Permutation may also refer to the particular arrangement of pieces itself.

Permutation may deal with both the positions and orientations of pieces, or sometimes just the positions only. For example, the following sequence permutes 3 corners, moving them into their correct positions, but disregards their orientations:

In group theory, a cube group permutation refers to both the positioning and orienting of pieces.

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