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.

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.