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George Duke wrote on 2011-01-19 UTC
Crying for attention are Triangles, not covered in Man&Beasts. In point (3) of this month's discussion, Gilman comments, ''It has been established that a board with triangles is a hex board with missing cells and pieces leaping holes.''  Triangles, like, and such as the comfortable, aesthetic two Bishop bindings there are not explained by any hexagon-based exposition so far.  Regular Hex comprised of six triangles within would not be the way to approach Triangular fundamentals. Rather, Triangles are virgin territory relatively, and Gilman just skips these the most important primitive connectivities of all. All sentient creatures, operate right up the ladder of importance: Triangles, Squares, and then the derivative lesser geometries (bird/ant navigation; lunar trajectories). True, art-design faddists have happened to like Hexagons for working cvs towards intellectual prestige.  Surrounding a regular hexagon in 2-d chess board/tiling are 6 hexagons making equilateral non-convex 18-side polygon. Certainly we do not opt for explaining the movement and jumping around ''hex board'' by that concave star-shaped isotoxal octadecagon the 7 hexagons subdivide.  Useful as far as they go, like earlier ''Multi-path Chess Pieces'' and ''Ideal and Practical Values,'' Man&Beasts articles can and do give false sense of completeness momentarily; but each step of the way in expansion of chapters leaves sense that only some lowly approximate-1% of potential ever is getting covered at all.  The peril of classification, catalogue, nomenclature.  In fact, the more names and piece-types, the more exponentially distant any goal of summation: Man&Beasts 9999. In other words, it is absolutely fatal flaw that Triangles are not covered, at the same time it will useless to do anything about it, incorporating them (the way Pentagons are now added, more or less a field birthed this past year).  Any correcting of the error is dooming effort to failure. Leave the hole, whistle in the dark; Nagual.

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