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George Duke wrote on Fri, Nov 12, 2010 04:19 PM UTC:Excellent ★★★★★
(1)What Rectahex comes down to needs no higher math or Betza master-skill spatial intuition. Simply put, sawtooth the board. That is, saw-tooth any rectangular board. Get the sides/edges how you want them artistically for however many squares. Now each interior square has six others adjacent, so it functions topologically hexagonally just as well even without deformation of the cell itself. Betza's article's end/beginning, ''Is hexagonal chess really hexagonal, or is it merely a rectangular dream?'' is so much poetical locution reflective of one combined state. Discard any construction half-fits left over from the work-ups, having slid and sized to requirement. In ideal material, actually just stretch and bend each square to a regular hexagon careful not violating even one adjacency. TOPOLOGICAL EQUIVALENCE. One size fits all. One board, and only one, serves both squares and hexagons of same number cells or smaller (black tape reductions). Make it 196 spaces of sawtooth 14x14 and that is 99.5% of the world's CVs ever made. _______________________________________________________________ (2) For purists over-the-board ideal material must needs be out there to shapeshift easily square-to-hexagon-to-square as rules-sets demand. CLAY takes some doing and Rectahex Ascii above shows is unnecessary routinely. For follow-up, how also can rectangles comprised of squares, whether or not saw-toothed, minimally disrupted, best reflect TRIANGULAR connectivity? This problem re-stated: We want not to draw a single triangle as such, yet have now more prevalent cultural squares represent them and their inter-connections accurately and completely. ___________________________(3) ENVOI. Thus squares may be at a crossroad, why Chess square-based remains. In the real world, more squares surpass circles and triangles for now, contrasted to superior antiquity (See Armies of Faith series). Just try stepping out to the market without an inefficient right-angle turn. Virtually impossible. Prevalent 90 degrees: house, room, that still monitor, blocked neighborhoods. Pourquoi? Obviously convenient states ''their'' Squares for control such that nary a soul be seeing/seen/scene/scheming/seeming around the corner.

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