## Sunday, October 6, 2013

### X-Cube Tutorial

The X-Cube is a beautiful twisty puzzle where the standard 3x3x3 cube has had an extra face attached to 4 of its sides. This puzzle shapeshifts, and makes some quite bizarre patterns. I'll be solving this cube by reducing it to a 5x5x3 cuboid, which I think is the simplest method to solve it. To buy this puzzle, click here.

The Basic Plot
2. Reduce Edges
3. Solve Reduced Cuboid

As a side-benefit of returning this puzzle to non-shapeshifted form, we'll solve the white and yellow 3x3 face centers as well. The edges can be placed using simple turns.

When we place the 3x3 corners, we'll also be flattening the pieces and will therefore take it out of shapeshifted form. The basic move is the corner piece series for cuboids, which is

(U R2 U' L2) x2

This will cycle UBL->DFL->DFR.

The only other thing we'll do to complete this stage, is to place the middle layer edge pieces, between the white and yellow faces.

It's a simple process, and involves turning the edge's position on its outer 3x3 face up to the top layer, move the edge into position, and turn the outer 3x3 face back down.

2. Reduce Edges

In speaking of the three edge pieces that need to be joined together, we can think of the puzzle as a cornerless-5x5x3. This means that we can treat the central edge plus the two adjoining corners, as an edge triplet which needs to be reduced.

To do so, we place an adjoining corner-edge 180° away from its center-edge, and then turn the puzzle to join them. This temporarily breaks the centers we've already done. Once the edge triplet is complete (or doublet if we can only do two pieces at a time), we use the edge piece series (U R2 U' R2) to move the completed edge onto an adjoining face, then return the messed-up centers. This is basically the same as the edge reduction on a 5x5x5 cube.

The only complication is that due to the puzzle having been shapeshifted, the "corners" can often be wrongly oriented. So that even if we bring pieces together, it won't complete the edge due to the wrong orientation. To get around this we place the corner on the opposite face, and then turn that face one turn. This changes its orientation and allows us to reduce the edges. We must of course remember to "unturn" this face at the end.

We reduce the edges in this manner until there are three left. Complete one of the last three edges as before. If both of the other edges are also completed, this stage is done.

If not, one of two scenarios will be in place.
1. A 3-cycle of corners
2. One swap of corners

To deal with a 3-cycle of corners, we use the corner piece series for cuboids (U R2 U' L2) x2 to cycle the pieces home.

To deal with a swap of corners, turn any of the outer faces one turn, and then re-place the two outer edges. This will fix the corner-swap but we will still need to re-reduce 3 or 4 of the edges. Once we have, we'll be left with a 3-cycle and can finish the edges as above.

3. Solve Reduced Cuboid

Stage 3 is the simplest and quickest stage of the solve.

First, we make sure the middle layer edges are correctly oriented. One or two twists will achieve this.

Next, we solve the reduced cuboid as though it were a 3x3x2 without corners, ignoring the middle layer.

As with a 3x3x2, it's possible to end up with two reduced edges needing to swap. The fix for this is to turn both the upper two layers one turn, then resolve the reduced edges.

And that's it. Your X-Cube 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. To buy this puzzle, click here.

1. Hello, very nice!
I used different approach, very similar to T-cube and L-cube but I like your more as it leverages this cube symmetries!
I did
- Shape
- Reduce edge/corners considering them as extensions of the 3x3x3 (with CPS like on L-cube)
- Do middle layer
- Solve as 3x3x2

I saw a full thread on twisty puzzles about different solutions to these, but I still have to read it more thoroughly ...

Good job

2. I can reach the stage where I only have 2 edges left, but then get stuck. I understand that there is then either a 3-cycle or a swap, but I can't seem to get the hang of what to do next. Is there a video which explains the basics of the 3-cycle (CPS) and the swap? I can follow the explanations for the traditional Rubik's cube, but I can't find anything similar for cuboids. Most of the videos seem to assume prior knowledge of the CPS and the swap. Many thanks.

3. I second Chris' post above. I can do CPS, but I can't understand the swap part - last paragraph of section 2. A more detail explanation or a video would be much appreciated!

4. I had a lot of trouble reducing a 2 or 4 cycle problem to a 3 cycle problem on the last edges.

If your on the second stage where you have two edges left put them on a top cross bit together. Do an Na or Nb alg as appropriate.

Algs that I found that are safe for the rest of the puzzle:

Na:
L2 F2 U2 F2 U' F2 L2 U2 L2 U' F2 U2 L2 U'

Nb

R2 F2 U2 F2 U F2 R2 U2 R2 U F2 U2 R2 U

U moves are just moving the 1x3x3 bit on top R2, F2, L2 are cutting 1 layer away from the center