Singmaster states that the diameter of the group for the 2x2x2 cube is not
known.

in his "cubic circular," issue(s) 5/6 (pages 26, 27) he gives some info
about this, although it is (at least) third hand information, and therefore
not necessarily reliable.

> I just did calculate it.
  ...
> If we allow half-turns:
>          1 with  0 moves
>          9 with  1 moves
>         54 with  2 moves
>        321 with  3 moves
>       1847 with  4 moves
>       9992 with  5 moves
>      50136 with  6 moves
>     227536 with  7 moves
>     870072 with  8 moves
>    1887748 with  9 moves
>     623800 with 10 moves
>       2644 with 11 moves

he gives the same figures, so they are probably correct.

If we do not allow half-turns:
         1 with  0 moves
         6 with  1 moves
        27 with  2 moves
       120 with  3 moves
       534 with  4 moves
      2256 with  5 moves
      8969 with  6 moves
     33058 with  7 moves
    114149 with  8 moves
    360508 with  9 moves
    930588 with 10 moves
   1350852 with 11 moves
    782536 with 12 moves
     90280 with 13 moves
       276 with 14 moves

he does not give these, but he does mention that the diameter is 14.

BTW, calculation did not take very long, only a few (<3) minutes on an FPS

singmaster says that the calculation took "over 51 hours of computer time"!
ouch! this was 10 years ago, though. (what's 51 hours / 3 minutes ?)

the "unix news item" from which singmaster apparently got his info was
included in a cube-lovers message. it's in the archives, cube-mail-3,
sept 15, 1981 in a message from "ISAACS at SRI-KL".

dik's results show that the corners of the 3x3x3 can be "solved" (i.e.
positioned correctly with respect to one another) in 11 face (respectively
14 quarter) turns. it would be nice to know if they can be solved with
respect to the centers within 11 face (respectively 14 quarter) turns.
this seems likely.

mike