Pocket Cube

Solved Pocket Cube.

Scrambled Pocket Cube.

Pocket Cube with one side tilted.

The Pocket Cube (also known as the Mini Cube) is the 2×2×2 equivalent of a Rubik's Cube. The cube consists of 8 corner pieces, and no other types of cubies.

Permutations

Any permutation of the 8 corner cubies is possible (8! positions), and 7 of the cubies can be independently rotated (3⁷ positions). There is nothing identifying the orientation of the cube in space, reducing the positions by a factor of 24. This is derived from the fact all 24 possible positions and orientations of the first corner are equivalent because of the lack of face centers. This factor does not appear when calculating the permutations of N×N×N cubes where N is odd, since those puzzles have fixed centers which identify the cube's spatial orientation. The number of possible positions of the cube is

${\frac {8!\times 3^{7}}{24}}=7!\times 3^{6}=3674160.$

The maximum number of turns required to solve the cube is up to 11 full turns, or up to 14 quarter turns. An optimal (least number of turns) solution from any position can be found by a computer with a brute force algorithm.

The number f of positions that require n full twists and number q of positions that require n quarter turn twists are:

n	f	q
0	1	1
1	9	6
2	54	27
3	321	120
4	1847	534
5	9992	2256
6	50136	8969
7	227536	33058
8	870072	114149
9	1887748	360508
10	623800	930588
11	2644	1350852
12	0	782536
13	0	90280
14	0	276

Records

Vicente Albíter of Mexico has the North American record of solving it in 1.55 seconds at the Mexican Open 2008

Erik Akkersdijk holds the current world record of solving the Pocket Cube in competition, with a time of 0.96 seconds set at the Geneva Open 2008.

For the best average time of 5 rounds, Rowe Hessler holds the current world record of 2.45 seconds set at the Brown Cubing Day 2009.

Variants

At Rubik's online store, an easier version of the Pocket Cube exists, dubbed the "Junior Cube". This version has only two colors, with a picture of a monkey on one face.

The Rubik's Ice Cube is a version of the Pocket Cube with transparent plastic and translucent stickers. It comes with a clear blue, ice-like display base.

The Eastsheen company produces a variation as well. It has a different, smoother-turning mechanism and is noticeably larger (5 cm) than the original.

Methods

There are several commonly used speed methods on the 2×2×2. The two most popular 2×2×2 specific speed methods are the Guimond and Ortega methods. Both of these methods have been proven to have the potential to break 5 seconds on average. Extremely fast but algorithm-heavy methods include the Stern-Sun (SS), Erik-Gunnar (EG), and CLL methods.

See also

• Pyramorphix, a pyramidal puzzle that uses the same mechanism
• Rubik's Cube (3×3×3)
• Rubik's Revenge (4×4×4)
• Professor's Cube (5×5×5)
• V-Cube 6 (6×6×6)
• V-Cube 7 (7×7×7)
• Speedcubing
• Combination puzzles