From:

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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