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It seems to me that a true tetrahedral form of chess would have 'cells' which, in three dimensions, would take the form of rhombic dodecahedrons, which would allow the board to be pyramidial with 'hexagonal' tiled layers. (Rhombic dodecahedrons tesselate space quite nicely, you know, and naturally lend themselves to making tetrahedra with.) Does the current setup of this game allow for such an analogue? The board can be easily translated, complete with cell coloration and the same twelve directions, but can the rules be translated as easily? I'd love to see an attempt.