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Transformations can be either simple rotations or a rotation composed
with a mirroring.
Simple rotations are denoted by two letters corresponding to the faces
to be moved to the U and F positions, respectively. For example FD is
the rotation that brings the F face on top and the D face on front.
A composed rotation + mirror is obtained by applying the corresponding
rotation to the solved cube mirrored along the M plane.
For example, to apply the transformation RBm (mirrored RB) to a cube C:
1a. Apply a mirror along the M plane to the solved cube
1b. Rotate the mirrored cube with z' y2
3. Apply the cube C to the transformed solved cube
4. Apply the transformations of step 1a and 1b in reverse
The orientation of pieces after a rotation ignores the new position
of centers. A rotated cube can technically be inconsistent, because
the parity of the edge permutation has to be adjusted considering the
parity of the centers, which we ignore.
The utility script mirror.sh transforms a solved, rotated cube to its
mirrored and rotated version.
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