Pyraminx notation
Pyraminx notation is the set of symbols used to indicate what moves to apply on a Pyraminx.
Contents
Turns
There are 4 faces on the Pyraminx. The puzzle should be held so that one face faces you and one face faces down, as in the image on the right. The four corners are then labeled U (for up), R (for right), L (for left), and B (for back). The front face thus contains the U, R, and L corners.
Normal Turns
A normal turn on the Pyraminx is actually a double-layer turn around a center, since single-layer turns only affect the tips and don't scramble the puzzle. There are two possible rotations for each move, which should be applied as if you are looking at the tip straight on: using the U center as an example, the moves are
- U for a clockwise turn of 120 degrees, and
- U' for a counter-clockwise turn of 120 degrees.
Notice that two U turns are equivalent to a U' turn, and two U' turns are equivalent to a U. Because of this, it isn't necessary to have notation for 'half turns' like on the 3x3.
Tip Turns
Turns of a tip (single-layer turns, that is) are denoted by a lowercase letter. The directions are the same as with normal turns. Since turning one tip does not affect any other pieces on the puzzle, and there are four tips, scrambles will have a maximum of four tip turns. These turns are never used in algorithms, and only in scrambling the puzzle.
Scrambling
Pyraminx is scrambled with the yellow face (if not possible, then the lightest face) on bottom and the green face (if not possible, then the darkest adjacent face) on the front. Moves are executed just as described above.
Example scramble:
4.
r' b u U' R B L' R' L' R' B' U' L R' U B' L U R' L' R B R' L' U' |
Here is the WCA-official Pyraminx scrambler, which is used for competitions.
Extensions to the Notation
First, there is no standard notation for face turns on the Pyraminx, but it is still useful to have a name for each face in case we want to describe specific edges. The names of the faces are as follows:
- F (front) is opposite to the B tip.
- R (right) is opposite to the L tip.
- L (left) is opposite to the R tip.
- D (down) is opposite to the U tip.
This means that the six edges are labeled RF, LF, DF, RD, LD, and RL (although these can be reversed on orientation, of course).
Extensions of the notation include:
- As we have seen above, face turns are not necessary for scrambling, and tip turns are not necessary for algorithms. Therefore, for algorithms, it is safe to use lowercase letters for face turns. This will be used to notate speed-optimized algorithms in some of the descriptions in this Wiki. So we will use f' for a counter-clockwise turn of the F face, and so on.
- Parentheses can be used to mark an edge that changes orientation during an algorithm (for example, (FR)).
- To prevent regrips in certain algorithms, it is also useful to create a notation for "half turns", such as R2 or R2'. This means the same thing as it does on a normal cube, that is, R2 is equivalent to two R turns and so on.
- When we want to rotate the puzzle during an algorithm, we can use a notation like oR to indicate orienting the puzzle (clockwise) around the R corner.
- Square brackets, such as in [x y], can be used to notate turns that can be done at once. This is often used for combinations of turning and orienting at the same time.
Here is an example algorithm, with different ways to execute it:
- R B R B' R - Normal notation. You have to change your grip in order to do three R's in a row.
- [R' l'] L R L' l ... The same algorithm, but with a different notation, using no regrips.
- [R2' oR] L R L' [oR' R] ... This is the same thing as the second algorithm, but instead of using face turns we have written it with puzzle rotations.
Another extension system
- L,R,U,B = Normal turns around the labeled axis
- Lw,Rw,Fw,Dw = Face turns of the labeled face
- [L,R,U,B] = Rotations around the labeled axis, (for instance [U] acts like a y rotation for 3x3x3)
2-flip can then be notated like this:
- L R' L' Lw L' R L R'
- Dw' R' Dw R' Dw R Dw' B
- [R'] L' R L' R' Rw R' L' R