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George Duke wrote on Sun, Jun 28, 2009 07:36 PM UTC:
Not interested in speculative ''far-ranging'' conversations with no touchstone but self-interest, that belong in Game Courier scores, where they also detract, I am set to emphasize analysis. Please continue in Philosophy and later some succinct couple sentences may sum up a week's talk. (1) Gilman has at least 5 geometries: square, hexagonal, cubic, hex-prism, tetrahedral. The goal is to describe hex-prism and tetrahedral with some same depth as Gilman. (2) Simplicities having gotten lost in discussion: one-stepper cubic through faces is Wazir, diagonals Ferz, triagonals Viceroy. FO versions of these are Point, Cross, and Saltire. (3) One-stepper rank-switching Silver General cannot triangulate in squares. Gold General is Wazir + Cross. Silver General is Ferz + Point. The latter is in cubes, where rank-switching does not necessarily prevent triangulation. Colourbound Ferz cannot triangulate in squares, but cubic Ferz triangulates. On hex boards Unicorn and Viceroy are clearly bound to 1/3, and that holds for hex-prism because by themselves there is no provision to switch levels. (4) In practice of designing 3-D CVs -- not particularly upheld by Gilman's nomenclative system -- we recommend for these simplest radials in a piece-type solo directions of Wazir-Rook, or else Ferz-Bishop, or else Viceroy-Unicorn; or all three at once in (probably) powerful piece. Using only two directions in a radial compound, (o+d), or (o+t), or (d+t) will lessen clarity whenas piece-types other than simple radials admit to the congregation.

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