Pocket Cube
Encyclopedia
The Pocket Cube is the 2×2×2 equivalent of a Rubik's Cube
. The cube consists of 8 pieces, all corners.
Any permutation
of the eight corners is possible (8!
positions), and seven of the them 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 because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed 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
The maximum number of turns required to solve the cube is up to 11 full turns, or up to 14 quarter turns.
The number f of positions that require n full twists and number q of positions that require n quarter turn twists are:
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. Rowe Hessler tied this record at the US Nationals 2010. For the best average time of 5 solves, Feliks Zemdegs
holds the world record with a time of 2.12 seconds set at Melbourne Cube day 2010.
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 turning mechanism and is noticeably larger (5 cm (2 in)) than the original.
Verdes Innovations has released the V-Cube 2, which is available in two shapes. The flat-sided V-Cube 2 is roughly the same size as the Eastsheen cube. The V-Cube 2b has a rounded shape like the V-Cube 7
.
Rubik's Cube
Rubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
. The cube consists of 8 pieces, all corners.
Permutations
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...
of the eight corners is possible (8!
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
positions), and seven of the them can be independently rotated
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...
(37 positions). There is nothing identifying the orientation
Orientation (geometry)
In geometry the orientation, angular position, or attitude of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it is in....
of the cube in space, reducing the positions by a factor of 24. This is because all 24 possible positions and orientations of the first corner are equivalent due to the lack of fixed 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
The maximum number of turns required to solve the cube is up to 11 full turns, or up to 14 quarter turns.
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
Erik AkkersdijkErik Akkersdijk
Erik Akkersdijk is a Dutch Rubik's Cube speedsolver.In 2008, he set several world records in Rubik's Cube, including the standard 3x3x3 cube....
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. Rowe Hessler tied this record at the US Nationals 2010. For the best average time of 5 solves, Feliks Zemdegs
Feliks Zemdegs
Feliks Zemdegs is an Australian Rubik's Cube speedsolver. The surname is Latvian.He bought his first cube in April 2008 inspired by speedcubing videos and tutorials on Youtube. The first unofficial time he recorded was an average of 19.73 seconds on 14 June 2008...
holds the world record with a time of 2.12 seconds set at Melbourne Cube day 2010.
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 turning mechanism and is noticeably larger (5 cm (2 in)) than the original.
Verdes Innovations has released the V-Cube 2, which is available in two shapes. The flat-sided V-Cube 2 is roughly the same size as the Eastsheen cube. The V-Cube 2b has a rounded shape like the V-Cube 7
V-Cube 7
The V-Cube 7 is the 7×7×7 version of Rubik's Cube. It was invented by Panagiotis Verdes and is produced by his company, Verdes Innovations SA. Like the 5×5×5, the V-Cube 7 has both fixed and movable center facets.- Mechanics :...
.
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
- PyramorphixPyramorphixThe Pyramorphix is a tetrahedral puzzle similar to the Rubik's Cube. It has a total of 8 movable pieces to rearrange, compared to the 20 of the Rubik's cube. Though it looks like a simpler version of the Pyraminx, it is an edge-turning puzzle with the mechanism identical to that of the Pocket...
, a pyramidal puzzle that uses the same mechanism - Rubik's CubeRubik's CubeRubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...
(3×3×3) - Rubik's RevengeRubik's RevengeThe Rubik's Revenge is the 4×4×4 version of Rubik's Cube. Invented by Péter Sebestény, the Rubik's Revenge was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube...
(4×4×4) - Professor's CubeProfessor's CubeThe Professor's Cube is a mechanical puzzle, a 5×5×5 version of the Rubik's Cube. It has qualities in common with both the original 3×3×3 Rubik's Cube and the 4×4×4 Rubik's Revenge, and knowing the solution to either can help when working on the 5×5×5 cube....
(5×5×5) - V-Cube 6V-Cube 6The V-Cube 6 is the 6×6×6 version of Rubik's Cube. Unlike the original puzzle , it has no fixed facets: the center facets are free to move to different positions...
(6×6×6) - V-Cube 7V-Cube 7The V-Cube 7 is the 7×7×7 version of Rubik's Cube. It was invented by Panagiotis Verdes and is produced by his company, Verdes Innovations SA. Like the 5×5×5, the V-Cube 7 has both fixed and movable center facets.- Mechanics :...
(7×7×7) - SpeedcubingSpeedcubingSpeedcubing is the activity of solving a Rubik's Cube or related puzzle as quickly as possible...
- Combination puzzlesCombination puzzlesA combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. The puzzle is solved by achieving a particular combination starting from a random combination...