From:

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I wish to withdraw, for the time being, my proposed answer to Dan

Hoey's question about how large is the cube group when symmetries

are taken into account. Notwithstanding two rounds of "correction",

I believe my proposal is fundamentally incorrect, and it will take

some time to come up with something better.

I believe that my proposed approximation is incorrect by a factor

of 24. That is, my proposed approximation would be correct for

corners plus edges (without centers), but would need to be

multiplied by 24 in order to be correct for corners plus edges

(with centers). My proposed approximation was

4.3 * 10^19 / (24*24*2). I now believe it should be

4.3 * 10^19 / (24 * 2), with the former figure correct only if

centers are omitted.

Secondly, I believe that my proposed procedure to calculate an

exact value from the known sizes of corner and edge groups is

incorrect. My procedure would be correct if all equivalence classes

had exactly 1152 elements. But they don't. It is not presently

clear to me whether the size of the equivalence classes when

corners and edges are combined can be calculated from the known

sizes of equivalence classes for corners and edges separately,

or whether a computer search will have to be performed for the

case where corners and edges are combined.

I will get back to this in a week or two. In the meantime, my

apologies if I have wasted your time, and I look forward to

any words of wisdom that any of you all might have.

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = Robert G. Bryan (Jerry Bryan) (304) 293-5192 Associate Director, WVNET (304) 293-5540 fax 837 Chestnut Ridge Road BRYAN@WVNVM Morgantown, WV 26505 BRYAN@WVNVM.WVNET.EDU

If you don't have time to do it right today, what makes you think you are

going to have time to do it over again tomorrow?