## Saturday, May 11, 2013

### 6x6x4

The 6x6x4 is a twisty puzzle which is a cuboid when solved, but which can shapeshift when scrambled. The one I'm using is a beautiful handmade version made by Traiphum. It is an absolutely superb puzzle.

The Basic Plot

2. Solve the Centers
3. Reduce the Edges
4. Solve the Reduced Cuboid

The first stage in solving this puzzle is to return it to a cuboid form, rather than shapeshifted form. To do this simply, we will make use of the corner piece series for cuboids. This sequence is (U R2 U' L2) x 2, but it has many variants according to which slices are turned.

Here are the steps which form the basic solve outline...

1. Solve the 2x2 centers on the white/yellow faces.
2. Make white/yellow edge pairs according to piece type, not colour.
3. Place these pairs on the top and bottom faces so that those faces have flat edges.
4. Flatten the 2nd slice pieces.
5. Flatten the outer slice pieces.
6. Move middle layer pieces on the top and bottom faces into the middle layer.

By now, the puzzle will be in correctly reduced cuboid form.

If the above steps seem difficult, they are not. Please watch the video below where I go through all the above and (hopefully) make things very clear and simple.

Step 2: Solve Centers

We now have a scrambled but non-shapeshifted 6x6x4. The next step is to solve the centers.

To solve the middle centers, make quartets of inner layer "edges". This is done just as we'll do it for the outer edges later. Once they're made, the white/yellow centers will be disrupted. So we move the newly made middle layer quintets onto another face, then return centers. The process is analogous to that done on a 6x6x6.

Then solve the white/yellow centers, with as many simple turns as possible, but also using the corner piece series variants to place the different piece types.

Step 3: Reduce Edges

To reduce the edges, follow the same procedure as above, but this time turn the outer face only on top and bottom.

The interesting part of this solve is the parity case which can occur. This will only occur when the puzzle has returned from a shapeshifted form. It shows up when the final two edge pieces need to swap. It is not possible to fix this without either a long-and-hard-to-memorise algorithm, or else a way of understanding what's going on and working from there. I choose to avoid the algorithm.

We have a single swap of edges. But in fact we can create an edge 3-cycle, which we can then deal with using the corner piece series. Creating the edge 3-cycle requires placing another edge of the same colour into the correct position, which will require the cuboid going into shapeshifted form briefly. It will return to cuboid form after we've carried out the edge 3-cycle.

The video below will help you to reduce all edges easily and to understand how to deal with the edge swap parity.

Step 4: Solve the Reduced Cuboid

At this point, we have reduced the puzzle to what is essentially a 3x3x2. To complete the solve, we

1. Place the middle centers
2. Place the middle outer edges.
3. Place the reduced edge quartets.
4. Place the corners.
All of this is done using simple turns and of course, the corner piece series. It's pure relief after the slog to get to this point.

However, as this is an even numbered cuboid, there is of course the chance that 2 corners will need swapping. This cannot be achieved using the ordinary corner piece series.

To swap the corners, we need only

1. Turn the upper face one turn
2. Re-solve middle outer edges
3. Re-solve corners

This video will show the entire process, including how to easily swap corners.

And that's it. Your 6x6x4 is now solved. I trust this site has been helpful. If you have any questions or want some clarifications, please use the comments to do so.