How to solve SQUARE-1 (Rubik's Variation) Cube?
Cube view
Definitions
During aplying transformations described below, fixed part must stay visible. Fixed part position must stay constant according to the puzzle solver (you). Each transformation consists of moves. Moves coding is as follows: n,m are integers (in general, they can be negative, zero or positive). N represents upper slice rotation and m represents lower slice rotation. We will use clockwise rotations for positive integers and counterclockwise rotations for negative integers. Integer n means, we will rotate upper slice clockwise, until we do not get the n-th available position for swapping (note, that there are 8 available positions for each slice, when the cube is in its cube shape). Note, when n=m=0 or n=m=8, we do nothing. After rotations, we can swap upper and lower half-slices. Note, that every transformation consists of x moves, where x is even integer. Formal definition of move: n upper slice clockwise rotations, m lower slice clockwise rotations and half-slices swap.
We will presuppose, that puzzle solver is able to put the cube into its cube shape. This elementary transformations are trivial. The next presupposition is, that puzzle solver is able to switch lower and upper slice. It can be done easily by 2-moves transformation. It is recommended to write down all 2-moves transformations they are cube-self-preservating.
Now, let's look at the transformations table (which can be obtained by writing a simple program analyzing possible operations). There are some edges transformations, corners transformations and mixed transformations (swaps two edges and two corners at once). There are two possibilities (or states), when you are finishing: all colors and pieces match. This is the happy case. The second state is, there are only two edges to swap. In this case, we need to switch cube's parity (i.e. switch from a state belonging to one half of its total states, to another state, belonging to the another half of its total states). This can be done by special transformation. It consists of three steps: fan creation, parity switching and cube restoration. After this, continue as before to finish the cube.
Transformations Table
| Edges transformations | Moves sequences |
 |
11
11 11 21 31 13 |
 |
51
11 11 12 22 22 |
 |
61
11 11 53 82 33 |
 |
61
11 11 11 11 42 11 33 33 11 |
 |
21
51 71 46 |
 |
21
31 71 66 |
 |
21
11 71 86 |
 |
11
22 81 53 |
 |
11
22 41 53 |
 |
61
11 11 11 31 42 13 33 13 11 |
 |
61
11 11 53 73 51 |
 |
11
11 11 21 31 22 |
| Corners transformations | |
 |
11
11 11 12 22 22 |
 |
55
11 11 12 31 13 |
 |
21
31 53 84 |
 |
21
11 53 82 |
 |
11
22 23 35 |
 |
21
51 53 86 |
 |
11
22 21 35 |
 |
11
22 41 35 |
 |
11
22 61 35 |
| Mixed transformations | |
 |
11
14 21 31 23 21 |
 |
21
28 22 42 24 42 |
| Special transformation | |
| How to swap 2 edges only ? | fan creation
00 13 -11 -21 parity switching -20 02 -14 -20 cube restoration -20 2-1 1-1 -1-3 continue as before... |