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George Duke wrote on Thu, Feb 17, 2011 04:15 PM UTC:
Okay this is mostly a correction before Charles or Ben. Okay, folding a newspaper confirms a1 slots into k10, j1 to t10, t1 to j10, k1 to a10, and so on. Continuing correcting the last comment, s1 meets i10 and r1 h10. The shift is a steady 180 degrees. (162 or 144 degrees could be another geometry.) Pawn of the last comment traverses e9-e10-o1-02-03 instead. The long leap lengths of the article are not useful compared to just seeing the geometry. Probably the leaps are all accurate, but only the Knight-components cannot be blocked. (Gilman once stated epiphanicly he finally ''saw'' Tetrahedral fully, so that lies ahead.) D.Q.B. wants it that way, that is all of its joins with the key 1/2 fold, because it is appropriate for Pawns to promote towards the opposition. Bishop still has same 4 directions. However, from departure to arrival square, Bishop can actually make it without two blocks, not one, strategically intervening. That is tantamount to saying Bishop is two-path to any square. In Cylindrical, Bishop is not two-path; whereas Torus with pi-twist, Bishop is two-path; and in Torus, Bishop is so sometimes only. Examples on Torus pi-twisted: (1) c6-d7-e8 (2) c6-b5-a4-t3-s2-r1-g10-f9-e8; (1) c6-d5-e4 (2) c6-b7-a8-t9-s10-h1-g2-f3-e4. So also is Rook two-path in Torus with pi twist. Can humans better than machines visualize these ''morphologies'' in order to move counters on the board sharply. Not likely. Now earlier cvs in their turn of related geometry can show how original the boards are with Gilman cvs, but for now ignore the D.Q.B. Intro links.

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