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Jun 14, 2012 at 14:25 comment added whuber There's also a deeper symmetry: the game is reversible and the roles of spaces and pieces can be reversed, too.
Jun 13, 2012 at 17:27 comment added Dr. belisarius @Sjoerd I think the Dihedral group D4/8 is a good candidate
Jun 13, 2012 at 14:50 history edited Dr. belisarius CC BY-SA 3.0
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Jun 13, 2012 at 14:48 comment added Dr. belisarius @Sjoerd And there there are also reflection symmetries ...
Jun 13, 2012 at 14:36 comment added Sjoerd C. de Vries I thought about isomorphisms too. With the four-fold rotation symmetry of the starting position that would be a natural thing to do. I didn't go that way because it is my intuition that later on in the combinatorial explosion of this game symmetry will be less prominent and you don't gain sufficiently by pruning them. I may be wrong there.
Jun 13, 2012 at 1:04 history answered Dr. belisarius CC BY-SA 3.0