Greg Strong wrote on Wed, Oct 2, 2013 09:10 PM EDT:
Upon further reflection, the rotational symmetry allows White to push the King's pawn but Black can't respond with the same move. (I'm not sure this is a balance problem, but people certainly wouldn't like it.) Here's another possibility that only swaps the Chancellor/Lion. It's not pure mirror or rotational symmetry, which I'm not sure has ever been done before, but I don't see anything wrong with it...
Upon further reflection, the rotational symmetry allows White to push the King's pawn but Black can't respond with the same move. (I'm not sure this is a balance problem, but people certainly wouldn't like it.) Here's another possibility that only swaps the Chancellor/Lion. It's not pure mirror or rotational symmetry, which I'm not sure has ever been done before, but I don't see anything wrong with it...
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