MI4
(Method and name still kind of a work in progress) This method is essentially the big cube version of Nautilus. Besides that, it is designed to fulfill two purposes. The first is to have a method that is completely direct solving with an option to also use reduction. The second is to remove blind spots early. I've always thought that OBLBL was an interesting way of blockbuilding on big cubes. At the same time I didn't like that it can be difficult to differentiate between the two front and back wings when building each slice and that unsolved centers and edges can be on the bottom and back of the cube. This means look-ahead is hindered. So in this method, the B and D centers and the DB edge is solved early to avoid these problems. First the direct solving method is described. After that the reduction option will be detailed.
Direct Solve Method
Step 1
Solve the left and right centers and the 1x3x4 on the left.
Step 2
Build the 3x3x3 block in the back. Some good blockbuilding strategies for the 3x3x3 include:
Build the right side 1x3x3 using the current freedom of movement. Then solve the B and D centers and the DB edge.
Solve the B and D centers, pair and add the DB edge, then build the right side 1x3x3.
Build a bar of two B centers, a bar of two D centers, and add the wing that goes between the two center bars. Do this for the other two center bars and wing or the rest of the layers up to the R layer for bigger cubes. Then add the right side 1x3x3.
Solve the D center, add the two lines on the B layer consisting of two vertical centers and an edge, then build the right side 1x3x3. This idea was suggested by Shrihari Kavale and based on a video of a method by Sam Fang.
An extended version of the above. Solve DR edge and D center then add the three lines on the B layer.
Step 3
Solve the remaining pieces below the LL. This involves new blockbuilding techniques that aren't seen in other big cube methods. My preferred way is to add 1x1x3 lines starting from the left. Another good strategy may be to make the F center then add the two edges and DFR corner.
Step 4
Solve the last layer. The LL method in Akimoto and K4 has been proven to be fast and is what I recommend. The steps are CLL > Two edges > Last two edges.
Direct Solve + Reduction Mix
Step 1
Solve the left and right centers and the 1x3x4 on the left.
Step 2
Build the 3x3x3 block in the back.
Step 3
Solve the U and F centers.
Step 4
Pair remaining edges.
Step 5
Finish as a 3x3. This is where the method really connects with Nautilus. The solve matches and ends best if Nautilus is used. However, it is easy to add DFM + DFR then finish as F2L.
Additional Blockbuilding
If the user wants to use more blockbuilding in the solve and not end with as much edge pairing, there are options. For step 3, instead of just solving the B and D centers and the DB edge, the two edges and the corner on the right can be solved. This extends the block all the way to the right.
Center bars along the front and their associated wings can also be solved up to the half-way point of the cube. If this is done early, it reduces the amount of effort required while building the final two centers and pairing the remaining edges.
The two above can be combined to leave a cube half-way point LS+LL state. This means that much of the rest of the solve is only r, R, and U moves.
This additional blockbuilding doesn't hinder the center building in step 4 or the edge pairing in step 5. The final wing or wings at DF would be paired in place.
