The
VCube 6
Contents 1 Mechanics 1.1 Permutations 2 Solutions 3 Records 4 See also 5 References 6 Further reading 7 External links Mechanics[edit]
VCube 6
Solved The puzzle consists of 152 pieces ("cubies") on the surface. There are
also 60 movable pieces entirely hidden within the interior of the
cube, as well as six fixed pieces attached to the central "spider"
frame. The
VCube 7
The
VCube 6
There are 8 corners, 48 edges and 96 centers. Any permutation of the corners is possible, including odd permutations. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving 8!×37 combinations. There are 96 centers, consisting of four sets of 24 pieces each. Within each set there are four centers of each color. Centers from one set cannot be exchanged with those from another set. Each set can be arranged in 24! different ways. Assuming that the four centers of each color in each set are indistinguishable, the number of permutations is reduced to 24!/(246) arrangements. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given color. This is raised to the sixth power because there are six colors. The total number of center permutations is the permutations of a single set raised to the fourth power, 24!4/(2424). There are 48 edges, consisting of 24 inner and 24 outer edges. These cannot be flipped (because the internal shape of the pieces is asymmetrical), nor can an inner edge exchange places with an outer edge. The four edges in each matching quartet are distinguishable, since corresponding edges are mirror images of each other. Any permutation of the edges in each set is possible, including odd permutations, giving 24! arrangements for each set or 24!2 total, regardless of the position or orientation any other pieces. Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced by a factor of 24. This is because the 24 possible positions and orientations of the first corner are equivalent because of 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. This gives a total number of permutations of 8 ! × 3 7 × 24 ! 6 24 25 ≈ 1.57 × 10 116 displaystyle frac 8!times 3^ 7 times 24!^ 6 24^ 25 approx 1.57times 10^ 116 The entire number is 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 887 168 573 442 107 637 760 000 000 000 000 000 000 000 000 (around 157 novemdecillion on the long scale or 157 septentrigintillion on the short scale).[3] One of the center pieces is marked with a V, which distinguishes it from the other three in its set. This increases the number of patterns by a factor of four to 6.29×10116, although any of the four possible positions for this piece could be regarded as correct. Disassembled Solutions[edit] This section possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (January 2013) (Learn how and when to remove this template message) There are a number of methods that can be used to solve a VCube 6.
One method is to first group the center pieces of common colors
together, then to match up edges that show the same two colors. Once
this is done, turning only the outer layers of the cube allows it to
be solved like a 3×3×3 cube. However, certain positions that cannot
be solved on a standard 3×3×3 cube may be reached. For instance, a
single quartet of edges may be inverted, or the cube may appear to
have an odd permutation (that is, two pieces must be swapped, which is
not possible on the 3×3×3 cube). These situations are known as
parity errors, and require special algorithms to be solved.[3]
Another similar approach to solving this cube is to first pair the
edges, and then the centers. This, too, is vulnerable to the parity
errors described above.
Other methods solve the cube by solving a cross and the centers, but
not solving any of the edges and corners not needed for the cross,
then the other edges would be placed similar to the 3x3x3 Fridrich
method.
Some methods are designed to avoid the parity errors described above.
For instance, solving the corners and edges first and the centers last
would avoid such parity errors. Once the rest of the cube is solved,
any permutation of the center pieces can be solved. Note that it is
possible to apparently exchange a pair of face centers by cycling 3
face centers, two of which are visually identical.
Records[edit]
The world record 6x6x6 solve is 1 minute, 19.60 seconds, set by Max
Park of
United States
Pocket Cube
References[edit] ^ 6×6×6 cubes at The Cubicle.us
^
United States
Further reading[edit] Rubik's Revenge: The Simplest Solution (Book) by William L. Mason External links[edit] Verdes Innovations SA Official site.
Frank Morris takes on the VCube 6
United States
v t e Rubik's Cube Puzzle inventors Ernő Rubik Uwe Mèffert Tony Fisher Panagiotis Verdes Oskar van Deventer Rubik's Cubes Overview 2×2×2 (Pocket Cube) 3×3×3 (Rubik's Cube) 4×4×4 (Rubik's Revenge) 5×5×5 (Professor's Cube) 6×6×6 (VCube 6) 7×7×7 (VCube 7) 8×8×8 (VCube 8) Cubic variations Helicopter Cube Skewb Square 1 Sudoku Cube NineColour Cube Void Cube Noncubic variations Tetrahedron Pyraminx
Pyraminx
Octahedron
Skewb
Dodecahedron
Megaminx
Icosahedron Impossiball Dogic Great dodecahedron Alexander's Star Truncated icosahedron Tuttminx Cuboid
Floppy Cube
Virtual variations (>3D) MagicCube4D MagicCube5D MagicCube7D Magic 120cell Derivatives Missing Link Rubik's 360 Rubik's Clock Rubik's Magic Master Edition Rubik's Revolution Rubik's Snake Rubik's Triamid Rubik's Cheese Renowned solvers Erik Akkersdijk Yu Nakajima Bob Burton, Jr. Jessica Fridrich Chris Hardwick Rowe Hessler Leyan Lo Shotaro Makisumi Toby Mao Tyson Mao Frank Morris Lars Petrus Gilles Roux David Singmaster Ron van Bruchem Eric Limeback Anthony Michael Brooks Mats Valk Feliks Zemdegs Collin Burns Lucas Etter Solutions Speedsolving Speedcubing Methods Layer by Layer
CFOP
Mathematics God's algorithm
Superflip
Thistlethwaite's algorithm
Rubik's Cube
Official organization World Cube Association Related articles
Rubik's Cube
