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This item is a game information page
It belongs to categories: Orthodox chess, 
It was last modified on: 2002-11-01
 By Mark  Thompson. Tetrahedral Chess. Three dimensional variant with board in form of tetrahedron. (x7, Cells: 84) [All Comments] [Add Comment or Rating]
Mark Thompson wrote on 2004-01-09 UTC
Jared, I believe the cells of the board shown here are topologically connected in the same way as the rhombic dodecahedron tiling you mention. Only the topological form of the board is relevant to play, so I wouldn't think that the translated rules would be enlightening ... if I'm visualizing correctly what you have in mind, I think it would be far harder to understand what the game is about. The trouble is that in any diagram I can imagine, you can only see a cross-section of each level, which prevents the full geometric form of the 3D cell from being seen. If you have 3D raytracer software you might be able to demonstrate it. I'd be interested in seeing that too. The ideal thing would be a virtual reality board, that players would see by donning those goggles that present stereoscopic 3D images that you can see all sides of by moving your head. When those become commonplace I predict a lot of wonderful 3D games will get implemented on them. I still haven't seen that technology, but I hope someday to use them to play Renju on a 'tetrahedral' board of order 13 or so. Charles, I'm reading your post for about the tenth time and am starting to figure out what you're talking about. You say 'square roots' but I believe you mean 'squares.' The base 36 business was confusing to me but you're really just doing it for compactness, so you can indicate each distance (or its square root) by a single character. And your use of 'coprime' doesn't seem to match the meaning I understand by that word. But I'm interested to see that the cells to which a knight at your origin can move are all labelled as distance sqrt(3) from the origin - well, that would make sense, just as a FIDE knight's moves are all sqrt(5) in length. Okay, I'm starting to follow your arithmetic - and I'm surprised, I wouldn't have guessed that the centers of cells in a rhombic dodecahedral grid would have distances whose squares are integers - though now that you point it out, I don't see why not. I'm not sure how playable your proposals for Unicorns and Nightriders would be on this grid -- it seems to me that to give them sufficient scope to practice their powers the board would have to be considerably larger and so have a huge number of cells, and a IMO game whose board has too many cells becomes too complicated to be interesting, because the moves have so many consequences no human player can foresee them; hence, it turns into a game of chance rather than skill. However, many people disagree with me, and I would be glad to see other game developers try their hand at this grid. If you're inspired, go for it!