12 September 2018

DaYan Mercury Bermuda Cube

The DaYan company has come up with a fresh and imaginative series of puzzles with its Bermuda line. Its unusual configuration intrigued me so I bought the first and simplest, the Mercury (there are eight variants, all named after our Solar System's major planets).

Seen from the angle pictured below, it looks like an ordinary Fisher Cube (if you are thinking of getting a Mercury and you are unfamiliar with the Fisher cube, it might be advisable to get one of those first to get accustomed to its configuration).

DaYan Mercury Cube

Turn the cube over and we see what is special about it...

Dayan Mercury Cube showing bandaged face

The triangular centre changes the configuration of the cube such that the blue and red sides work as a standard cube with the other corner operating as a Fisher cube. This bandages the cube in an unusual way preventing certain turns that slice the white and yellow faces.

In the picture above, the triangular section can be rotated vertically; this is the only freedom of movement in the cube in terms of R- L- F and B-type moves. Rotate the top, yellow face by 45° and this releases the other sides of the triangle while locking the hypotenuse.

The cube moves easily and freely, provided it is lined up properly. Some care is needed to ensure the cube is aligned because it does pop more easily than it should do. The puzzle does corner but it is better, in my experience not to push it and care needs to be taken with the yellow face to ensure that it is turned correctly to allow smooth turning during a solve.

A scrambled puzzle quickly loses the integrity of its cube shape, which can make it confusing when performing algorithms and lining up it correctly to perform turns. This may be especially the case if you are unfamiliar with the Fisher cube.

Scrambled Mercury Cube

It offers a step up in challenge compared with the Fisher or standard configuration Rubik's cube but I did not find it overly difficult to solve.

Parity

One thing I had not anticipated when I first set out to solve this puzzle was the parity issue that is possible. Fortunately, DaYan provided a means to avoid it with the logo on the white sticker on the middle piece of the white face. Before scrambling the cube, look carefully at this face and orientation of the centre piece. During the solve, return the cube to the same orientation; if it is rotated by 90°, a parity issue will rear its ugly head and no one likes that mid-solve.

Solving the Mercury

Described below are the steps that I took to solve this puzzle. I don't know if it is the best way but it is the way that I do it. It has an elegance that I find pleasing. I am not going to include any algorithms but the steps below should provide enough clues for anyone who might be struggling with this puzzle. The algorithms that I used were standard algorithms adapted for this puzzle's configuration.

Step 1 - Partially Solve the White Face

Solve three of the white pentagonal piece and the triangles between them, leaving one side free...

Mercury Cube Solve Step 1

 



Step 2 - Orientate the Rectangular Pieces on the Middle Layer

Use the unsolved section to rotate all four rectangular pieces on the middle layer so that are all orientated correctly. Remember, these behave like centres on a regular cube.


Mercury Cube Step 2

Step 3 - Complete the White Face

Complete the white face. Care must be taken to preserve the orientation of the rectangular piece under the fourth pentangular piece. It is not quite as easy as it looks.

Mercury Cube Step 3

Step 4 - Solve the Squares on the Middle Layer

Manoeuvring them into the right positions is made more tricky by the bandaging on the yellow face but there are no orientation issues to worry about so it is not all bad. Remember the squares behave as edges. Care needs to be taken to leave the rectangular pieces in the correct orientation.

Mercury Cube Step 4

Step 5 - Solve the Rectangular and Pentagonal Pieces on the Yellow Face

Permutating and orientating the rectangular and pentagonal pieces on the yellow face is not difficult; they behave like edges.  Align the pentagonal piece with the green and orange faces. If the rectangular pieces are not in the correct places then there is a parity issue. The white face was not solved correctly. To fix this rotate the white centre by 90° and learn from your mistake! See Parity, above.

Mercury Cube Step 5


Step 6 - Solve the Yellow Triangles

Solve the yellow triangles. These pieces behave like corners. The small square pieces also behave like corners, so from a cube mechanism point of view, the yellow face has five corners.
It is possible to merely permute them and then orientate all of the pieces at the end but I prefer to do permutate and orientate these two pieces at this stage.

Mercury Cube Step 6

Step 7 - Solve the Yellow Squares

Finally, solve the yellow squares. These pieces both look and behave like corners. Manoeuvring the pieces into the correct position is not difficult but the bandaging of the yellow face limits options for rotating them into the correct orientation.

So there you have it, one solved Mercury Bermuda Cube.

Mercury Cube Step 7

Addendum

Updated 30 November 2018.
While playing with other Bermuda cubes a different solution for this puzzle popped into my head that is better than the route I describe above. It is more efficient and removes the possibility of a parity issue popping up to spoil the solve.

Step 1: Solve the Yellow Squares and Rectangles

An intuitive step.


Step 2: Orientate the Rectangles on the Middle Layer

Use the unsolved Fisher corner to rotate the rectangles of the middle layer to the correct orientation. These pieces behave like centres.


Step 3: Solve the Blue and Red Squares

These pieces behave like edges.
Completing this step creates a pseudo-Fisher style block.


Step 4: Orientate the Pentagons

It is not essential to do this step but it is easier to rotate them at this stage than later. Though they may go out of rotation later, or at least it is possible the way I do it.


Step 5: Complete the Yellow Face

The simplest way to do this is to the yellow pentagon first and then slot the triangles into position.

Step 6: Solve the Orange and Green Squares

This is a fairly simple step that should present few difficulties.
There is only the white face left to solve.


Step 7: Permutate the White Pentagons

This is a trivial step.


Step 8: Permutate the White Triangles

This can be done with familiar algorithms altered to take into account the bandaging on the yellow face.


Step 9: Orientate the White Triangles

Again, not a difficult step provided the bandaging of the yellow face is taken into consideration.

There we have it, a solved Mercury cube.


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