In a virtual exploded Rubik's cube, select one of the 3 orthogonal rotation axes, and select any 9 cubies such that they do not overlap when projected to the plane perpendicular to the selected rotation axis. Permute and rotate the cubies around the axis as if they all shared the same plane. Edges, corners, and face centers can all interchange. Center (core) remains in place.
This operation preserves the 90-degree rotation aesthetic of the original Rubik's cube.
The puzzle might be too easy with so many operations possible. Let each cubie not only have a correct orientation but also unique correct location.
Other dimensions, including 2.
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