For configurations where no faces can be solved with half-twists, another way of solving is to to place the cube so that there are vertical pairs of parallel corners on the front face and horizontal pairs on the back face as shown below (turn cube with mouse to see back face). The color of the pair in the top row of the back face (white in this case) must match the color of the pair on the right side of the front face, if it matches the left side then half-twist the front face to make the setup.

The sequence does not solve the corners, it makes them solvable with half-twists. This is not a new sequence, it is the first Starter Cube sequence done twice with the second applied from the back. The centers are not part of the setup and can be ignored. The other faces can also be ignored (do not have to match cube below).

If no faces have parallel pairs (all 3-1 splits) then half-twist the right face to make parallel pairs on either the front/back or top/bottom faces. On the first cube below, the first move makes parallel pairs on the front/back faces. The color of the pair in the top row of the back face is yellow so the front face is half-twisted (second move) to make the setup. An alternative would be to use the mirror-image sequence in which case the second move is not needed.

On the second cube, the first move makes parallel pairs on the top/bottom faces so the cube is turned (second move) so they are on the front/back faces with the vertical pairs in front. The color of the pair in the top row of the back face is red which matches the right side of the front face so the setup is correct.

Like the waterwheel this sequence also misplaces edge facelets when used on a cube where edges are already solved as 3-color. In this case four edges get misplaced but they can easily be fixed as shown here, this can be avoided by solving 6-color corners before 3-color edges.