The Skewb Diamond is an octahedron which is bisected 4 ways, by planes
in between and parallel to two opposite faces. Any face can be turned through
120 degrees in either direction, moving exactly half the puzzle. The puzzle
consists of 8 triangular face centre pieces and 6 corner pieces.
The Skewb Diamond is closely related to the Halpern-Meier Pyramid (see
Pyraminx) and the Skewb,
which also have 4 axes of rotation. The six corner pieces of the
Diamond correspond to the 6 edge pieces of the pyramid. The 8 face pieces of
the Diamond correspond to the corners and faces of the pyramid, except that
on the Diamond none of the face orientations are visible. Similarly, the six
corner pieces of the Diamond also correspond to the 6 face pieces of the
Skewb except that orientations are visible, and the 8 face pieces of the
Diamond correspond to the corners of the Skewb but without visible
My solutions for the Skewb will also solve the
Diamond. The solution below is slightly faster however.
Note that turning one face has the same effect on the puzzle as turning the
opposite face the other way. Therefore the puzzle can be solved by only using
one of each pair of opposite faces. Internally 4 of the face centres are fixed
on axes, and the other 4 are moving pieces. Externally there is no visible
difference between the two sets. In the solution below we will use only one
of these sets and call these the fixed face centres, and the other faces
are called the free face centres. This internal mechanism not only makes
clear that the two sets of face centres cannot be mixed together, it also
shows the corners have only two orientations.
The number of positions:
There are 4 fixed faces, 4 free faces, and 6 corner pieces with 2 orientations
giving a maximum of 6!·4!·26 positions. This limit is not reached because
- The corners must have an even permutation (2)
- The free faces must have an even permutation, and hence form a tetrad (2)
- The number of twisted corners must be even (2)
This leaves 6!·4!·26/8 = 138,240 positions.
A computer search gave the following result:
This shows that any position can be solved in at most 10 moves (6.6921 on average).
In Sloane's On-Line Encyclopedia of Integer Sequences
this is included as sequence
Links to other useful pages:
Uwe Mèffert's pages
has a solution here
Mèffert produces and sells this puzzle, the Pyraminx, Megaminx, Skewb, and many others.
Diamond with one face at the front with one corner pointing upwards. The set
of 4 fixed faces that you will use in solving the puzzle lie on the down, left and
right sides (adjacent to the front face) and the back side (opposite to the front).
You will only turn these four faces, not the others, and the fixed centres of these
faces show which colours these faces should have. Denote 120 degree clockwise
turns of the faces by L, R, D and B. Anti-clockwise turns are denoted L', R', D' and B'.
Any corner can be specified by two letters, e.g. DR is the corner where the down
and right faces meet. The 4 free face centres can similarly be specified by 3 letters.
Phase 1: Place the three top corners correctly.
- Find a corner piece in the D layer which belongs in the top layer. If there are no
such pieces, then choose any corner in the D layer to use to displace an
incorrectly placed corner from the top layer.
- Rotate the whole puzzle so that the corner piece belongs (or is to displace the
corner piece) at the LR position (the top front corner).
- Turn D to put the corner piece at the back (at DB).
- Do one of the following to place the piece in the correct position, with the
1. To move DB to LR, do R'D'R.
2. To move DB to RL, do LDL'.
If you choose the wrong one, you can use R'BD'RL' to flip the LR position in place.
This is also useful if in step a you only have flipped corners in the top layer.
Phase 2: Place the other three corners correctly.
- Rotate D to put its corners in position, though they may have the wrong
- If some corners in the D layer need to be twisted around, turn the puzzle
around the D axis so that the corners to be twisted lie at the front of the
puzzle (at DR, DL to be precise). Then do DL'BRB'L. The corners should now
Phase 3: Place the free face centres correctly.
- If one of the face centres is already correctly positioned, then hold
the Diamond so that the correct centre lies in the top face. The other
three centres need to be cycled around, and this is done by performing
the sequence LR'L'R'LR'L'R' to move them anti-clockwise around D, or
RLRL'RLRL' to move them clockwise.
- If none of the free face centres are correct then hold the diamond so
that the top and front centres need to be swapped around and do