I had intended to include the following table in my first
post concerning God's Algorithm for the 2x2x2 cube, but
I forgot. It addresses the question of how large are the
equivalence classes in the search tree, where the equivalence
classes are generated by the two rotational symmetry groups
and the one reflectional symmetry group. Most of the
equivalence classes have 24*24*2=1152 elements, but some have
fewer.

Size of          Number          Total Number
Equivalence       of              of
Class            Nodes           Permutations
                                 Represented

   24                 1                   24
   48                 1                   48
   72                 3                  216
   96                 1                   96
  144                14                2,016
  192                15                2,880
  288               135               38,880
  384                32               12,288
  576             2,208            1,271,808
1,152            75,392           86,851,584
 ----             -----             --------
Total            77,802           88,179,840

 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
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

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