grom358 / rubix

Rubix cube

Rubix cube

Overview

A rubix cube has six faces: Front (F), Back (B), Right (R), Left (L), Down (D), Up (U).

        B
     _______
    /      /|
   /  U   / |
L /______/  | R
  |      |  /
  |  F   | /
  |______|/

      D

Each face is a grid of 3x3 cubes. We refer to each face on a cube as a facelet. In 3D coordinates (x, y, z) the top left cube is (0, 0, 0).

Unfold the cube into 2D representation as follows:

  U
L F R B
  D

Then number the facelets as follows:

          00 01 02
          03 04 05
          06 07 08

09 10 11  18 19 20  27 28 29  36 37 38
12 13 14  21 22 23  30 31 32  39 40 41
15 16 17  24 25 26  33 34 35  42 43 44

          45 46 47
          48 49 50
          51 52 53

Starting from top-left cube facing the front face. Going left to right, top to bottom and front to back we number the cubes starting from 1.

Front:
01 02 03
04 05 06
07 08 09

Middle:
10 11 12
13    14
15 16 17

Back:
18 19 20
21 22 23
24 25 26

Moves

Moves are clockwise when looking at the face. Moves are marked with ’ suffix for counter clockwise rotation. Moves are:

L

Left face

R

Right face

U

Up face

D

Down face

F

Front face

B

Back face

M

Layer between L and R, turn direction same as L

E

Layer between U and D, turn direction same as D

S

Layer between F and B, turn direction same as F

X

Entire cube, turn direction same as R

Y

Entire cube, turn direction same as U

Z

Entire cube, turn direction same as F

u

Top two layers

d

Bottom two layers

r

Right two layers

l

Left two layers

f

Front two layers

b

Back two layers

Solve

1. Daisy. Start with yellow center on top. Form a daisy by bring the white edges to top. That is looking at top face:

   x W x
   W Y W
   x W x
       

2. White cross. Match the corresponding edge of the white edge with its matching center color. Turn that face 180 degrees. Repeat for all the white petals of the daisy. Now on the bottom should have a white cross.
3. White corners. Place a corner with white in the top-right-front position with its matching colors on the front and right face centers. For example, for the corner with White/Green/Orange have the front face with green center and right face with orange center. Then repeat the move combination (called sexy move) R U R’ U’ until the white face is facing downwards. Repeat for all white corners. After this step the bottom layer is complete.
4. Second layer. For this step you need to place the 4 edge pieces for the second layer into the correct position. For example, the Green/Orange edge piece between the orange and green centers. Match the outward facing edge with its matching center color. Rotate cube so this center is the front face. For example, if the top edge is Orange then the outward edge would be green and so we match the green edge with the green center. Look at the top edge and determine if the matching center color is on the left or right face. If on right perform the move U R U’ R’ U’ F’ U F otherwise U’ L’ U L U F U’ F’
5. Yellow cross. In this step we create a yellow cross on top face:

   x Y x
   Y Y Y
   x Y x
       

   There are 3 possible states to get to yellow state:

   1. dot

      x x x
      x Y x
      x x x
              

   2. L (align with edges in 9 and 12 oclock position)

      x Y x
      Y Y x
      x x x
              

   3. Line (align in horizontal position)

      x x x
      Y Y Y
      x x x
              

   Perform the combation move F U R U’ R’ F’ until you form yellow cross.

6. Yellow face. If there is one yellow corner align like so:

   x Y x
   Y Y Y
   Y Y x
       

   Otherwise position a yellow outward facing corner on top left:

     x Y x
     Y Y Y
   Y x Y x
       

   Perform the combination move R U R’ U R U2 R’

7. Orient yellow corners. We can swap the 2 right corners:

   x x A
   x x x
   x x B
       

   by using the combination move L’ U R U’ L U2 R’ U R U2 R’

8. Orient yellow edges. If one of the faces is complete make this face the back face. Looking at the edges you will need to either turn:
   1. Clockwise: F2 U R’ L F2 L’ R U F2
   2. Counterclockwise: F2 U’ R’ L F2 L’ R U’ F2

   If no face is complete perform either of the above to complete a face, then repeat this step.

9. Congratulations your rubix cube is now solved.

Implementation

The rubix cube is rendered using HTML elements with each cube being an element containing 6 children elements for each face of the cube. jQuery is used the manipulate the DOM to perform the rubix cube moves.

jQuery returns elements in DOM order. Therefore the cube is arranged in left to right, top to bottom, and back to front order.