*Not to be confused with the Diamond Cube.*

**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.

## DescriptionEdit

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.

It is very closely related to the Skewb, and shares the same piece count and mechanism. However, the triangular "corners" present on the Skewb have no visible orientation on the Skewb Diamond, and the square "centers" gain a visible orientation on the Skewb Diamond. Combining pieces from the two can either give you an unsolvable cuboctahedron or a compound of cube and octahedron with visible orientation on all pieces.

## Number of CombinationsEdit

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 2^{5}.

The number of combinations is therefore (4!/2)(6!/2)(2^{5})=(12)(360)(32)=138240. That is a lot of combinations, although nowhere near the number of the Rubik's Cube, which has 4.3x10^{19} combinations.