Step 3: Last Extended Slot (LXS)
Solve the remainder of the first two layers. The basic strategy is to solve the large front center then the triple at DR. This means the basic steps up to this point are first block, all centers, then the bottom triple. A simple and intuitive strategy is followed to solve the triple. The entire process makes use of three move motions to move and place centers - F' U F, F' U' F, BR U BR', or BR U' BR'. It works similarly to F2L last slot on 3x3 where an edge is easily placed into the last slot using one of the three move inserts - F' U F, F' U' F, R U R', or R U' R'.
Other techniques can be used at the advanced level to solve this step, including solving additional pieces with the front center and building large last slot groups.
Part 1: Front Center
In the first part of this step, solve the front center. Most of the same techniques used to solve the back center are used here.
Part 2: Last Triple
In the part 2, the last triple will be solved. This consists of the DR corner and its two unsolved centers.
First Center Piece
Before starting, try using any combination of F' U F, F' U' F, BR U BR', and BR U' BR'. Notice that it works just like the last slot on 3x3. Each of them move around the bottom triple and three U layer triples. The big U layer center stays in place. These simple motions are used to solve the bottom triple.
Start by finding the corner that belongs on the bottom layer. Check where its purple center is located. Then check if a purple center piece is on the opposite side.
1. Find the bottom layer corner then check where its purple sticker is located based on its orientation. The corner is on the U layer at the back right in the image. The purple sticker is on the back.
2. Next, ensure that a purple center piece is in pairing position on the opposite layer. The center is on the U layer at LF in the image.
3. Turn the R layer to pair the corner with the center piece. In the image, R' was used.
4. Move the pair to the correct side of the group of three B center pieces that are now on the U layer. Use simple separation moves to move the pair - F' U F, F' U' F, BR U BR', or BR U' BR'. In the image, F' U F was used.
5. Move the pair and center group over to the R layer and solve. The bottom yellow center will be solved next.
If a purple center piece isn't in pairing position at the start of the step, position a purple center piece using F' U F, F' U' F, BR U BR', or BR U' BR'. To keep the corner on the upper layer and in its current orientation, if the corner is at the upper front, use F' U F, F' U' F, BR U BR' U', or U BR U' BR'. If the corner is at the upper right, use F' U F, F' U' F, U BR U BR' U, or U' BR U' BR' U'.
Second Center Piece
1. Find the bottom center piece. In the image, the yellow center is at the LF position on the U layer.
2. Turn the R layer and move the pair and center group out of the way.
3. Move the yellow center over into position to be solved. The yellow center is on the left side of the corner that it is currently attached to, so BR U BR' or BR U' BR' will be used to solve the center.
4. Use the same separation moves to solve the bottom layer center without affecting the pair and center block. In the image, BR U BR' was used.
5. With the center solved, position the pair and center block and solve with R or R'. In the image, U R finished the first two layers.
If the DR corner is already paired with a center at the beginning of Part 1, the basic option is to pair with a new center. But there is a better way. First, solve the pair correctly in the F2L using one of the separation moves. Then, solve the D center using an adjustment of the R layer and one of the four separation moves.
Simultaneous Center Piece Solving
Solving the two centers can be a merged process. Solving the bottom layer center in Part 2 will always start with an R or R' move. This provides the opportunity to keep the initial pair and center block on the upper layer and make use of the freedom to solve the second center. The pair and center block can be solved to the last layer at the very end.
As an example, continue from step 4 of Part 1: First Center.
4. Instead of solving the pair and center block, locate the yellow bottom center. It is at the BL position. In the image, BR U BR' is used to solve the center.
5. Use the same separation moves to solve the bottom layer center without affecting the pair and center block. In the image, BR U BR' was used.
6. With the center solved, position the pair and center block and solve with R or R'. In the image, U R finished the first two layers.
Advanced Last Slot Building
When solving the last two centers, the ending will almost always be R U R' or R U' R'. At that point, the same three move algorithms can be used to position the corner and a purple center ready to be solved using the final R U R' or R U' R'. Once those pieces are in position, perform the initial R move to build the group of last slot pieces. Then solve the bottom center and add the pair and center block to the right side layer.
1. The final step of solving the centers often gives an appearance such as this.
2. Use the three move algorithms to position the corner in the front and center piece in the back.
3. Perform the initial R move to pair up the centers, simultaneously pairing the corner and center piece.
4. Locate the bottom layer center. In the image, it is at the LB position.
5. Solve the center piece using the same three move algorithms. In the image, F' U' F was used.
6. Move the pair and center block to the right side layer then finish.
If the bottom layer center piece is already solved at the start, or was intentionally solved with the front center's left trap, moves such as BR' F' U' F U BR cycle the U layer pieces without affecting the bottom layer center piece. F or BR' can be used to place an unsolved triple at the DR position to allow for free working of other pieces using the three move algorithms..
Algorithmic Triple
The three part triple solving process is easy and intuitive. However, it can be made more efficient by solving in a single step using algorithms. A document will be created containing all possible cases.
APB Style F2L
The last layer state can be reached by also using the steps of the Nautilus related method APB. In this style the steps are:
FB
Stripe - Solve the slice of the bottom two layers between the BL and R layers. This leaves the U and R layers unsolved. The bottom layer center piece can be either solved during this step or left out.
Solve the remainder of the first two layers. If following the APB steps exactly, the other half of the BR center is filled in then the five pieces of the last slot are solved. If the bottom layer center was left out during the second step, it can be easily solved during this step.
Last layer.
Nautilus is designed primarily for blind spot elimination and ease of look ahead. APB style contains more blind spots, so look ahead may not be as good as the primary Nautilus style.
