On 10/27/94 at 16:20:08 Ybanez Sheldon said:

Now since I joined this mailing list I have been inundated with all these
algorithms.... how do I translate them? Being a neophyte to cube
'theory' its pretty frustrating trying to figure out what all the letters
and numbers mean... and what they are trying to achieve....

can anyone help?

I was thinking of suggesting a few references, but then it occurs that
perhaps there are not very many references currently in print. Here
is a little Cube Theory 101.

In the "Standard Model" (or maybe the "Singmaster Model") of the 3x3x3
cube, the cube is not rotated in space. The only thing you can do is
twist one of the six faces. Singmaster designates the faces as
Up, Down, Right, Left, Front, and Back. The names are chosen so that
no two of the faces start with the same letter. There have been some
latter day efforts to rename Up as Top so that all the faces have names
beginning with consonants.

Twists are designated by the first letter of their name -- U, D, R, L,
F, and B for clockwise quarter-turns; U', D', R', L', F', and B' for
counter-clockwise quarter-turns; U2, D2, R2, L2, F2, and B2 for half-
turns (180 degrees). In proper typography, the "2" in "U2" is
written as a superscript. Sometimes U3, D3, etc. are used to denote
counter-clockwise quarter-turns because three clockwise quarter-turns
produce the same result as one counter-clockwise quarter-turn.

A sequence of twists is written left-to-right -- e.g., FRU'LLR.

The complement notation which is used to convert clockwise quarter-turns
into counter-clockwise quarter-turns may also be applied to a group
of twists -- e.g., (FRU')' is equal to UR'F' (twisting in the opposite
order and in the opposite direction).

The same sort of notation is used to describe cubies -- the up-right
cubie is ur. Singmaster distinguishes between cubies and cubicles
via italic and Roman text, but that is a bit hard to do via E-mail.

Things get a bit more complicated when you consider slice moves,
cubes larger than 3x3x3, and rotations of the whole cube. Note that
most people solving "real cubes" (as opposed to mathematical
models of cubes) do indeed rotate the whole cube, for example they
move the Bottom face to the Up (or Top), to make it easier to twist.
However, the "Standard Model" does not rotate the whole cube because
mathematically it is just as easy to twist one face as any other.

Hope this helps.

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Robert G. Bryan (Jerry Bryan)              (304) 293-5192
Associate Director, WVNET                  (304) 293-5540 fax
837 Chestnut Ridge Road                     BRYAN@WVNVM
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