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David Paulowich wrote on Mon, Jun 4, 2007 02:45 AM UTC:

Stephane Burkhart's Cross3D Chess is the 8x8x8 variant where this discussion started. I proposed [2005-08-22] a sort of 3D-Shatranj on a 6x6x6 board, with a weakened King (3D Wazir) that moved in only 6 directions.

Index to Ralph Betza's 3D Chess covers multiple approaches to 3D variant rules, with Kings and Commoners on 8x8x8 cells. I forget the details, but I believe there was a lack of 3D symmetry. 3D Chess: Major Topics includes: Three Dimensional Chess Endgames, where he states that King, Queen, and Commoner versus King is quite possibly a draw in the general case. But he considers King and Two Rooks versus King to be a forced win. That is very unusual in 3d chess variants.