Fused Cube

There are many ways a 3x3x3 Rubik's cube can be bandaged to make an interesting variant of the puzzle. One such way has been given a name: the fused cube. Simply put, a 2x2x2 corner of the cube is fused, leaving only 3 of the 6 faces free to rotate. We will let these be the R, U and F faces for the solution to follow. The RF, RU and FU edges will face you the entire time, as will the RFU corner.

Step 1

Solve edge cubies in the bottom layer.

Step 2

Solve the corners and edges in the first 2 layers in the FL and RB edges. I like to use the FR edge as a staging area for these edges. Solve position and orientation for these.

Step 3

Place the corner in the bottom layer in the RF edge. Ignore orientation. Don't worry about the middle layer edge cubie in the RF edge. We solve that in step 5.

Step 4

Now permute the corners in the top layer into their proper positions, ignoring orientation. I use U,R,Ui,Li,U,Ri,Ui,L, pretending we have a regular 3x3x3. Of course, when you execute L or Li, the middle layer is going along with it. No worries.

Step 5

Position the last edge cubie in the middle layer and RF edge, ignoring orientation. To do this while preserving all corner cubie positions, I setup the top layer with the needed rotation, then use R,2[R,U,Ri,U,R,2U,Ri],Ri.

Step 6

Now position the edge cubies in the top layer. Use 2[R,U,Ri,U,R,2U,Ri] with the needed setups.

Step 7

Lastly, orient all cubies in the top layer, and the edge and corner cubies in the RF edge. Only one sequence is needed for all of this, and it is A=Ui,R,U,2R,F,R,2F,U,F,Ui with proper setups, which may include something like |RFU|. Notice that 2A orients corners, but not edge cubies; and 3A orients edge cubies, but not corners. Just use A by itself to orient corners or edges first, then take care of the other.