rich schroeppel asks

Has anyone tabulated the number of positions are reachable (from the
initial cube) in one move, two moves, etc.? Is the diameter of the
graph known?

first note that there are two common ways to define a "move",
any twist of a face (face turn metric), or any 90 degree turn
of a face (quarter turn metric).

jerry bryan was counting (and storing) positions close to start
on magnetic tape. he gave figures for positions within 7 face
turns on july 19, 1994 and positions within 11 quarter turns on
february 4, 1995. (jerry, how many reels of tape did this take?)

the diameter isn't known. the best lower bounds are 20 face turns,
or 24 quarter turns, both from considering the position "superflip".
the best upper bounds are 29 face turns, or 42 quarter turns.

mike