There are three parts to the Rubik's Cube page, one is the Cube itself, one is the Faces applet, and then at the bottom there is the Notation applet. Since the Notation is the important part, I'll go into it first.
I used the standard Singmaster notation which is composed of the following commands:
f | rotate the front face clockwise |
---|---|
b | rotate the back face clockwise |
l | rotate the left face clockwise |
r | rotate the right face clockwise |
u | rotate the up face clockwise |
d | rotate the down face clockwise |
Thus if you were to type:
F | rotate the cube around the front face clockwise |
---|---|
B | rotate the cube around the back face clockwise |
L | rotate the cube around the left face clockwise |
R | rotate the cube around the right face clockwise |
U | rotate the cube around the up face clockwise |
D | rotate the cube around the down face clockwise |
The capital letters mean to rotate the entire cube under the
face entered. This changes what the face specified by
the lower case commands moves.
For Example:
Note- the color of a face is determined by looking at the center cube on that face, since the center cubes never move in relation to one another, nor do they change places.
Now comes exponentiation. Exponentiation is done by using the ^ symbol. (That should be shift-6 on most keyboards.) Exponentiation can do a number of different things. For instance r^2 means do r twice, or rr. (ur)^2 means (ur)(ur) or urur. Thus exponentiation to a positive exponent means repeat exponent times.
However, exponentiation to a negative exponent is also allowed. r^-1 means turn the right face counter-clockwise. Note that on the Cube, r^-1 is the same as r^3 or rrr. This of course means that r^-2 means the same thing as r^2, both mean turn the right face twice, and on the cube two turns in one direction is the same as two turns in the other direction.
Negative exponentiation for a set of commands in parenthesis is even more complicated. (ur)^-1 does not mean u^-1r^-1, in fact negative exponentiation means you must reverse the order of the commands as well as their direction. Thus: (ur)^-1 means the same as r^-1u^-1. This is and important feature because it means that (ur)(ur)^-1 actually doesn't change anything, since it translates to urr^-1u^-1.
Note- I'm now going to use the shorthand command+ to mean command, and command- to mean command^-1 i.e. r+ means r, and r- means r^-1. This is how the computer outputs the translation, however this notation cannot be used to input commands.
The ^ is an overloaded symbol, which means that it does more than just exponentiation. It you have a command exponent integer, than the program does exponentiation, however, if you have a command exponent symbol command, than the exponentiation symbol becomes the conjugate symbol. Conjugation means the following: r^b becomes brb^-1, i.e. conjugation in general is, x^y means xyx^-1, and thus (ur)^(dl) becomes (dl)(ur)(dl)^-1 or d+l+u+r+l-d-.
Well, there is only one command left to go. Commutation. The commutator is made up of [,]. It works in the following: [u,r] means uru^-1r^-1 or in general [x,y] means xyx^-1y^-1.
Now all of the above commands can be combined in different ways, thus you could do something like [u,l^(fd)]^-1 which becomes f+d+l+d-f-u+f+d+l-d-f-u- (But that's not obvious. Try it and see.)
Here's an example I came up with randomly that turns out to be a really neat move, try it and see: (r^b[l,u^b]r^b)^4
You now know all the symbols.
() | parenthesis |
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^ | exponentation or conjugation |
[,] | commutator |
Variables
For example;
Now you can use y as if it were one of the moves from above, such as y^2, or y^u, etc. After you type in a variable declaration, if it is legal, it will be added to the variables box, so that you can see it if you forget what it stands for. As well you can assign variables to other previously declared variables, i.e x=y^-1. However you can't do x=j, since j hasn't been defined.
Note- spaces can be used in the Notation editor, and are ignored, however a space before a variable name declaration, or the equals sign won't work (i.e x = doesn't work, but x= does).
The commands on the cube are simple. The mouse can rotate the cube in the x and y directions, it takes a little while to get used to. If you click on the Cube and then press space bar the cube should scramble itself. If you press the Shift button and then click on a face of the Cube, that face will rotate clockwise. If you press Control and then click on a face that face will rotate counter-clockwise. Note that for some reason, these moves are really slow on my version of the applet. (I made a few alterations to his program, but not many.)
This should cover all of the necessary instructions on how to use the Notation applet and Rubik's Cube. If you have anymore questions, or think this page needs further clarification, please email me.