From: McKeeman at PARC-MAXC
Subject: Re: nomenclature
In-reply-to: DDYER's message of 9 Jan 1981 1648-PST
To: Dave Dyer <DDYER at USC-ISIB>, VaughanW.REFLECS at HI-Multics (Bill
 Vaughan)
cc: cube-lovers at MIT-MC

I agree there are two problems:
  1.  Neat "programs" that allow the recording and carrying out of manipulations.
  2.  Neat "configurations" that allow the recording of the results of carrying out
manipulations.
In both cases uniqueness, transparanecy, conciseness and all other notational
goodies are appropriate.

Generalizing a bit on Dave's suggestion, how about:

Manipulation = Macro*
Macro = MacroName "=" Move*
Move = Move "*" Integer                  -- power
        | Move '                              -- inverse
        | Move / Move                      -- conjugate
        | MacroName
        | Face (Near (Middle Far?)?)?      -- hand moves
        | "(" Move* ")"                       -- parenthesization
Face = F | U | R
Near = Middle = Far = 0 | 1 | 2 | 3

with considerate use of spaces and carriage control.  Face signifies "temporarily
move that face into the right hand, do the moves, then move it back where it
came from".  For compatibility, the digits count QTW clockwise (away).

The FLUBRD equivalences are:

R=R=R1=R10=R100
RR = R*2
RRR = R*3 = R'
L=R003
U=U
D=U003
F=F
B=F003
Slice=R01
AntiSlice=R103
I=F111
J=R111
X Y X' = Y/X

Note this has some chance of generalizing to other slice puzzles.  (E.g. 4x4x4)   It
also subsumes FLUBRD with a few appropriate Macro definitions like those
above.

------

For configurations the problem can be attacked by specifying which cubies go to
which cubies.  Singmaster does some of this.  The problem is to find a way to
specify patterns of change without just listing all the changes.  There are
positional change, flipping and rotating to be accounted for.

For instance, we would like to say (in some much neater way)

EdgeFlip = For all X and Y in FLUBRD, edge XY goes to edge YX.
The corners each take one step on a Hamilton path.
Each corner is rotated 120o.
Each center exchanges with its opposit.
Each edge XY goes to UV where U is the opposit of X and V is the opposit of Y.
Etcetera, etcetera, etc.


BFUDRLy yours,

Bill