Date:  6 AUG 1980 0939-EDT
From: JURGEN at MIT-MC (Jon David Callas)
Subject: Random Notes on Cubism
To: CUBE-LOVERS at MIT-MC
CC: JURGEN at MIT-MC

I am beginning to feel competant enough to jump into the fray, so ...
1)	language: I guess that RLUDFB has become the de facto lg. for cubing.
(by the way, how IS 'RLUDFB' pronounced?) Is this to include the IJK rotations
that ACW described on 7-19? They are very handy, but I know that there is a desire tokeep the lq. brief. Also what (if anything is being done with the center
slices that Bernie used while describing the higher crosses? Given RLUDFB+IJK
notation,  they are easy algorithms (subroutines?) that can be described as:

	FPC {floor-parallel center} := udK
	BPC {body-|| center}	    := fbI
	BSC {body-slicing center}   := rlJ

without IJK, they're much more complex. Perhaps this is a case for using
RLUDFB & IJK.

	2) I have been playing a little with the group of rotations, twists
 and so forth. I thought that it mighht be very wieldy until I remembered that Don Woods has given us a transform with period 1260. (Is it just my
imagination or is 1260 important? it seems like a familiar number) This means
(by la Grange's thm ) that the order of this group is some integral multiple
of 1260 (ugh!) That eliminates hand-enumerating (at least by me) it. How
much does anyone else know about this, and are thre any interesting subgroups?
It also seems that this thing might be related in some way to the dihedral gps.
but I'm not sure.

	3)Somewhat connected with (2) above, it would be nice if we compiled
"Famous Transforms I Have Known" or something to that effect. Not only would
it help in finding my desired sbgp, but it would help keep some of the
folklore out of cubing (while there is nothing wrong with folklore,
there are problems when falsities (especially VERY inobvious ones) creep
into the body of lore. Folklore also does tend to cause duplication of
effort and that most of us have probably been wasting time re-inventing
the Pons Ansinorum (which, by the way, IS 'rrllffbbuudd', isn't it?)
Since I'm suggesting this nonesense, I guess it's only fair to
volunteer to do this compendium (unless someone else is dying to).

	4) Would it be possible to modify :cube to work on a
printing tty? I really don't care if it produces large volumes of paper.
I am avoiding implementing my own form of a Cube program on my
APPLE ][ (see my notes above on duplication of effort), if I can
get away with using :cube, but at least the Apple display will be pretty.

	5) There MUST be a better way to check for an impossible cube
than solving for it. While there is no shame in solving a bad cube,
there IS a little embarassment, and there certainly is no honor in it , either.
Besides, the anti-intuitionist part of me finds solving-as-proof distasteful.

	6) Has any one taken 'Rubik's Cube ' apart? I have tried prying
the edge cubie as mentioned, and all I did is hurt my thumb. I'm afriad
to use any sort of tool, lest I break the little beast.

	7) Can we get a Cubing Bibliography, including Singmaster's articles,
and the Games & Puzzles article and anything else anyone finds? (ONce
again, since I suggested it, I'll do it if need be.)

	8) Are Singmaster's 'orbits' REAL permutation-group type orbits,
or just equivalence classes? I'm confused by his choice of words.

				-happy cubing,
					Jurgen@mc