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Charles Gilman wrote on 2011-04-03 UTC
It looks like the tri-hexagonal geometry is a kite that can fly (pause for groans). As well as the Rook curving round on itself, I notice that the Knight and Camel can triangulate. Assuming the three-player-variant rules for Bishop movement where six quadrilaterals meet, the Bishop and Ferz can reach every cell and the Ferz too can triangulate. The Elephant, Tripper, et cetera appear bound to single diagonals as there is no continuation of three-player-variant diagonal steps.

Another group of pieces that look interesting in this geometry are those that are non-Straight in the square geometry (see Man and Beast 09). The Girlscout has a straighter path than the circuitous Rook, and alternates not between two Bishop paths but between one Bishop path and one path alternating orthogonal and diagonal steps. The Boyscout has a very strange path, bifurcating at each meeting of six cells. The Rhino moves seemes to get cut a bit short in its Crooked form, but takes a curious oblong circuit, still of eight steps, in its Curved (Leaping Bat Chess) form.

Note that I am not considering geometries with cells of different shapes - should I say this explicitly, do you think?

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