Welcome to the Chair of Technology and Innovation Management

Rubik's Cube 2 x 2 x 2

Rubik's 2 x 2 x 2 Cube consists of eight corner “cubelets”. The chart shows a plan of a state of the cube. The first row represents the top, the second row the left, front, and right side, and the third and forth row the bottom and back side, respectively.

Without loss of generality, hold the cube so that the white/red/blue cubelet is the top-left-back corner at position 0. The white facelet of this cubelet points upward. Given this convention, only moves of the right side (denoted by ↑ and ↓), the front (↱ and ↰) or the bottom (← and →) need to be considered.

Whatever the state of the cube is, the page calculates how to solve the cube with the lowest number of moves.

Move the Cube

Set Explicit State of the Cube

Clicking on the arrows, will perform respective moves.

				↑
			0	3
			1	2
	0	1	1	2	2	3
←	4	5	5	6	6	7	→
		↱	5	6	↰
			4	7
			4	7
			0	3
				↓

Expand the dialog of a position to select a particular cubelet that is to switch positions with the current cubelet. After the switch, the white or yellow facelet of the cubelet selected to move will point upward or downward (whatever will be applicable). The other cubelet will be rotated such that the state of the cube is feasible.

A positive rotation (“+”) is a counterclockwise twist of the cubelet without changing its position. Similarly, a negative (“-”) rotation is a twist in the direction of the clock.

Rotating only one cubelet is not possible. Total rotation of any state and the total roation of the solution must always be congruent modulo 3. Any rotation of a cubelet will cause the cubelet on position 7 to perform the respective counter-rotation.

Position	Cubie	Rotation
0	◼-◼-◼ The cubelet on position 0 is fix.	White facelet always points upward.
1	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
2	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
3	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
4	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
5	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
6	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼
7	◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼ ◼-◼-◼	Rotation is set automatically.

The above cube is solved.

Provided free of charge for scientific purposes.
Hosting: Chair of Technology and Innovation Management, Universität Bayreuth, Bayreuth, Germany.
© Universität Bayreuth, Lehrstuhl für Technologie- und Innovationsmanagement.