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
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?