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Kevin Pacey wrote on Sun, Feb 12, 2017 11:02 PM UTC:

Hi Joe

I think a knight in my hexagonal variant idea can reach the centre hex on the centre board, or leave it, provided I (as planned) use for knight movement rules an analogue of Hyperchess4 Knight movement (as I understand it works with square cells or 2D boards). That's since a knight can move orthogonally to a different 2D Hexagonal board that's just one or two 2D boards away orthogonally (i.e. in 4D). When a knight leaves from a centre hex, I'd have the knight arrive only two or one cells orthogonally away from the centre hex (on a cell that must be of a different basic colour than the knight started on), on the destination 2D board. Note that from the centre hex of the centre 2D board I indeed could not make an entirely BIG move, i.e. to a centre hex of a new 2D board that would be (if it were possible) just a BIG knight move away, as I think you are alluding to (besides that a knight cannot reach a centre hex by moving on the same 2D board, which I alluded to earlier too). The fact a rather 'impure' knight's tour is the only kind possible makes the variant idea a little more ugly, perhaps, but I didn't mind, in order to try to have a more reasonable 4D board size that's still hexagonal in all respects.

I'm going to check my current ideas a little more, then very soon I may post a diagram for it in my diagram testing thread, to study it even more closely at leisure.

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