Skewb Diamond

The Skewb Diamond is an octahedron-shaped puzzle similar to the Rubik's Cube. It has 14 movable pieces which can be rearranged in a total of 138,240 possible combinations. This puzzle is the dual polyhedron of the Skewb.

Description

The Skewb Diamond has 6 octahedral corner pieces and 8 triangular face centers. All pieces can move relative to each other. It is a "deep-cut" puzzle: its planes of rotation bisect it.

Number of combinations

The purpose of the puzzle is to scramble its colors, and then restore it to its original solved state.

The puzzle has 6 corner pieces and 8 face centers. The positions of four of the face centers is completely determined by the positions of the other 4 face centers, and only even permutations of such positions are possible, so the number of arrangements of face centers is only 4!/2. Each face center has only a single orientation.

Only even permutations of the corner pieces are possible, so the number of possible arrangements of corner pieces is 6!/2. Each corner has two possible orientations (it is not possible to change their orientation by 90° without disassembling the puzzle), but the orientation of the last corner is determined by the other 5. Hence, the number of possible corner orientations is 2⁵.

Hence, the number of possible combinations is:

:$frac\{4!\; imes\; 6!\; imes\; 2^5\}\{4\}\; =\; 138,240.$

See also

*Rubik's cube
*Pyraminx
*Megaminx
*Skewb
*Dogic
*Combination puzzles
*Mechanical puzzles

External links

* [http://www.geocities.com/jaapsch/puzzles/diamond.htm Jaap's Skewb Diamond page]