THE EDGE PIECE SERIES
In this approach to solving a scrambled Rubik's Cube all 12 edge pieces are placed first. The first four are placed in Step One which is straightforward. Some of the others are moved into place with a simple replacement process. The remainder utilize a symmetric four turn series which moves three edge pieces around a corner of the cube.
The red face of the cube in Fig. 1a is front.The red/yellow edge piece at front/top belongs at front/right. We cannot simply rotate the front face clockwise by 90o because we have already placed four blue edge pieces on the bottom face and would not want to move any one of them out of place. But an Edge Piece Series will move the red/yellow, orange/yellow and red/green edge pieces around the front/right/top corner of the cube without moving other edge pieces. (These edge pieces have been numbered #1, #2 and #3.) According to standard notation this series is F R' F' R.
Fig. 1a Fig. 1b
Applying this series gives the cube shown in Fig. 1b. We find that edge piece #1 is now in the position originally occupied by edge piece #2. That is, #1 replaced #2. Further, #2 replaced #3 and #3 replaced #1. The three pieces moved about the front/top/right corner of the cube in a counterclockwise direction. The blue edge pieces on the bottom of the cube are undisturbed. Some corner pieces have also moved but that is immaterial. At this time we are interested only in the movement of edge pieces.
We can also describe this series in terms of the movement of edge pieces #1, #2 and #3.
Turn one Front clockwise #1 replaces #2
Turn two Right counterclockwise #3 replaces #1
Turn three Front counterclockwise reverse turn one
Turn four Right clockwise reverse turn two
Now let us consider what has happened to these edge pieces. If the front face in Fig. 1b is turned 90o counterclockwise we find that edge piece #1 (red/yellow) has the same orientation as before. The same is true of edge piece #2 (turn the right face 90o counterclockwise). But edge piece #3 is different. If we turn the top face 90o counterclockwise we find that edge piece #3 has been inverted.
This is always true of these edge pieces. Edge pieces #1 and #2 are not inverted while edge piece #3 is inverted. You are free to number the three edge pieces in any way you want to. Then, provided you always follow the turn sequence given above, you will find that #1 replaces #2, #2 replaces #3 and #3 replaces #1. Edge pieces #1 and #2 will not invert while #3 inverts.
Look at the cube in Fig. 2a. This is the same cube as in Fig 1a except that the top face has been turned 90o in a counterclockwise direction. We still want the red/yellow edge piece to move into the front/right position. But to be properly placed it must invert. Hence it must be edge piece #3. Since #3 replaces #1 then orange/yellow must be edge piece #1. Green/white then is edge piece #2.
Fig. 2a Fig. 2b
We will apply the series as before.
turn one #1 replaces #2
turn two #3 replaces #1
turn three reverse turn one
turn four reverse turn two
Now examine the result, the cube in Fig. 2b. Again we have accomplished our main purpose, the movement of the red/yellow edge piece into its proper position and orientation at front/right. The orange/yellow piece is involved in both instances but it moves to a different location. However, red/green is involved in the first case while the green/white piece has replaced it in the second series. In the second example, the three pieces have moved in a clockwise direction about the front/right/top corner of the cube.
The red/yellow edge piece may be moved into its correct position/orientation from a position above either the red or the yellow center pieces by an Edge Piece Series. Which version of the series you will want to use will depend on what else you are trying to accomplish. We will visit this situation again in Step Two of the Ultimate Solution to Rubik's Cube.
Go to the Corner Piece Series