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Actually, I think 8x8 is about the smallest possible 2D board for chess. Realistically, of square boards, 6x6 is the smallest that you can have a game on that approaches chess. As far as higher dimensions, I know [beyond reasonable doubt] that 256 squares, 4x4x4x4, is the smallest 4D board that you can play a high-quality game of chess on, with regular pieces. [Okay, Parton's Sphinx Chess is on a 4x4x3x3, but if you play the Java applet, you'll see the 9 4x4 boards are a bit too small; he juggles the setup and some knight moves.] For 3D, I suspect the smallest really decent board size is 6x6x6. These sizes are all based on using more or less standard FIDE pieces and moves.