Fig. 6a
STEP THREE: THE TOP EDGE PIECES
In this section we will place the fourth center section edge piece and the four top edge pieces in their proper positions and orientation.
At the conclusion of Step Two, three top edge pieces were to have their top color on the top face of the cube. Those three edge pieces could be in any one of the following possible arrangements:
1. All three could be out of order.
2. Two adjacent pieces could be in the proper order relative to each other with the third out of order.
3. Two opposite pieces could be in the proper order relative to each other with the third out of order.
4. All three could be in the correct order relative to each other.
The three white edge pieces on the top of the cube in Fig. 6a are all out of order. Note that the top edge piece face you cannot see on the back of the cube must be red. If the top face of the cube is turned 90o clockwise then the yellow face of white/yellow would be adjacent to the yellow face center and white/yellow would be in the proper position/orientation.
Fig. 6a
But neither of the other two white edge pieces would be in the correct position. The green color would be above the red face center and the red color would be above the orange face center. No matter which of the three top edge pieces is put into place the other two will be out of place.
We can correct this by applying an Edge Piece Series to the cube. However, the series must involve three top (white) edge pieces. Rotate the top face until three white edge pieces are adjacent to the top/front/right corner as they are in Fig. 6a. The cube obtained by rotating the top face 90o clockwise would also be suitable.
Always be sure that three white pieces are in the series and that it concludes with three white faces on top of the cube. In all cases the white edge piece in the center section will be edge piece #1. In Fig. 6a white/orange will be #1 and white/yellow will be #2. Any other choice would not leave three white edge pieces with their white faces on top of the cube at the end of the series. This series will change the top edge pieces to one of the other arrangements.
In the case of the cube in Fig. 6a the series converts it to the cube in Fig. 6b. Here two adjacent edge pieces are in the proper order (white/yellow and white/orange) and one is out of order (white/red where red is above green). These pieces may be put in the proper order by turning the top face by 180o and applying an Edge Piece Series to the top edge piece in the center section (white/green), the top edge piece which is out of order on the top face (the white/red piece) and the fourth center section edge piece (yellow/orange). The latter is moved into proper position/orientation and all four top edge pieces will be in their proper order. A 90o counterclockwise turn of the top face will put all top edge pieces in their proper place. Step Three is complete.
Fig. 6b
Fig. 6c
In the third case two opposite edge pieces are in position relative to each other and the third is out of place as shown in Fig. 6c. The white/yellow top edge piece is in place. By the process of elimination the color you cannot see on the white edge piece is green. Since the green face on my cube is opposite the yellow face the white/green piece must also be in its proper place. But the white/red piece is out of place. It belongs on the other side of the top face.
The white/orange piece belongs where the white/red is now. The former can be put there by a simple 90o rotation (clockwise) of the orange face. Turn the top face by 180o and a 90o counterclockwise turn of the orange face will move the white/red edge piece back to the top face and into its proper position relative to the other three. Finally another 180o turn of the top face moves all white edge pieces into place. Step Three is complete.
In the fourth case all three top edge pieces on the top face are in their proper position relative to each other. This is shown in Fig. 6d. The unseen color of the white edge piece is red and it clearly is in the red face of the cube. This arrangement is converted to one in which all four white edge pieces are in the proper order on the top face by a series of replacements.
Fig. 6d
Fig. 6e
Fig. 6f
We begin by replacing a white edge piece on either end of the three on the top face with the white edge piece in the center section. For example, rotate the top face in Fig. 6d by 90o clockwise giving Fig. 6e. Rotate the green face 90o clockwise giving Fig. 6f. The white/red piece is replaced by the white/yellow piece and the former moves to the center section.
Now turn the top face 90o counterclockwise (Fig. 6g) and replace the white/green piece with the white/red piece (i.e. rotate the green face by 90o counterclockwise) to give the cube shown in Fig. 6h. Continue in this fashion until, in the fourth turn of the green face the last white edge piece (in this case the white/orange piece) returns to the top face of the cube and the fourth center section edge piece moves into place at front/right.
Fig. 6g
Fig. 6h
You might ask how one knows that the fourth center section edge piece has the proper orientation and is not inverted. While you made sure that the top edge pieces had their white color on top you did nothing to ensure that the center section edge piece had the proper orientation. This is true for each of these examples. But you don't need to worry about the 12th edge piece. If 11 edge pieces are in the proper position and orientation then the 12th must be in the proper position and have the proper orientation as well. It cannot be otherwise.
Turn the top face so that all top edge pieces are in position (in this case 90o clockwise). Step Three is complete and all edge pieces have been properly positioned/oriented.