Notation

Notes on notation:

There are six sides to the cube, known as Front, Back, Left, Right, Up and Down. They are usually referred to by their one-letter abbreviations (see the figures below).

In the diagrams below, you see the F, R and U sides. The F faces to the left.

Movements are presented as one quarter rotation (90 degrees) of an external face per movement. This means that the center tile colors are not changed. In our diagrams, F is blue, R is red and U is yellow. The other three colors are typically orange (we use magenta, which is a lot more different from yellow) opposite red, green opposite blue and white opposite yellow

In order to display what is happening on the sides of the other three colors, the cube can be rotated as a whole

1.F	2.R	3.D
4.B	5.L	6.U

Quarter-rotations of that face's layer default to clockwise. Counter-clockwise rotations are often referred to as "inverted" and indicated by <, e.g. R<.
The < is commonly read as "prime", "anti-clockwise", "anti" or "i" for inverted.
*** Note that we use < in place of the 'usual' ' to avoid having to put 2 symbols '', instead of just one, in Matlab strings.
Half-rotations (180 degrees) are indicated by the digit "2". For instance, R2 (meaning 2 quarter-rotations).

Finally to describe mathematically the rotations, we define the x, y, z space axes as follows:
x is the lower edge of the face R, and points to the right of the page in the default view.
y is the lower edge of the face F, and points to the left of the page in the default view.
z is the edge between the faces F and R, and points upward in the default view.

A convenient numbering of the faces, very compatible with the above definition of the x, y, z space axes, greatly simplifies the code - making it flexible and straightforward.