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My last comment was a quick correction/explanation of what I had said before. Now that I have had some time to think offline I can comment on the idea of splitting the the orthogonals into two groups of three. The truth is, any such division is arbitrary. They naturally divide into three groups of two - those in the horizontal plane, and those in the vertical plane through each horizontal diagonal. In fact these planes are interchangeable, each having 2 orthgonals of its own and two diagonals each shared with one of the other two. However limiting pieces to those pairs of orthogonals binds them to single planes, and even limiting them to the two orthgonals in a plane and the diagonal outside it would bind them to alternate planes. The oddity that the root-three (hex) diagonal is not colourbound on this board is matched by the root-two (square) diagonal is not colourbound on a hex-prism board.